Orthonormal systems and Banach space geometry /:
Orthonormal Systems and Banach Space Geometry describes the interplay between orthonormal expansions and Banach space geometry. Using harmonic analysis as a starting platform, classical inequalities and special functions are used to study orthonormal systems leading to an understanding of the advant...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
©1998.
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications ;
v. 70. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Orthonormal Systems and Banach Space Geometry describes the interplay between orthonormal expansions and Banach space geometry. Using harmonic analysis as a starting platform, classical inequalities and special functions are used to study orthonormal systems leading to an understanding of the advantages of systems consisting of characters on compact Abelian groups. Probabilistic concepts such as random variables and martingales are employed and Ramsey's theorem is used to study the theory of super-reflexivity. The text yields a detailed insight into concepts including type and co-type of Banach spaces, B-convexity, super-reflexivity, the vector-valued Fourier transform, the vector-valued Hilbert transform and the unconditionality property for martingale differences (UMD). A long list of unsolved problems is included as a starting point for research. This book should be accessible to graduate students and researchers with some basic knowledge of Banach space theory, real analysis, probability and algebra. |
| Beschreibung: | 1 online resource (ix, 553 pages) : illustrations. |
| Bibliographie: | Includes bibliographical references (pages 523-545) and index. |
| ISBN: | 9781107089105 1107089107 9780511526145 0511526148 |
Internformat
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| 245 | 1 | 0 | |a Orthonormal systems and Banach space geometry / |c Albrecht Pietsch & Jörg Wenzel. |
| 260 | |a Cambridge : |b Cambridge University Press, |c ©1998. | ||
| 300 | |a 1 online resource (ix, 553 pages) : |b illustrations. | ||
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| 490 | 1 | |a Encyclopedia of mathematics and its applications ; |v v. 70 | |
| 504 | |a Includes bibliographical references (pages 523-545) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a Orthonormal Systems and Banach Space Geometry describes the interplay between orthonormal expansions and Banach space geometry. Using harmonic analysis as a starting platform, classical inequalities and special functions are used to study orthonormal systems leading to an understanding of the advantages of systems consisting of characters on compact Abelian groups. Probabilistic concepts such as random variables and martingales are employed and Ramsey's theorem is used to study the theory of super-reflexivity. The text yields a detailed insight into concepts including type and co-type of Banach spaces, B-convexity, super-reflexivity, the vector-valued Fourier transform, the vector-valued Hilbert transform and the unconditionality property for martingale differences (UMD). A long list of unsolved problems is included as a starting point for research. This book should be accessible to graduate students and researchers with some basic knowledge of Banach space theory, real analysis, probability and algebra. | ||
| 505 | 0 | |a Cover; Half-title; Title; Copyright; Contents; Preface; Introduction; 0 Preliminaries; 0.1 Banach spaces and operators; 0.2 Finite dimensional spaces and operators; 0.3 Classical sequence spaces; 0.4 Classical function spaces; 0.5 Lorentz spaces; 0.6 Interpolation methods; 0.7 Summation operators; 0.8 Finite representability and ultrapowers; 0.9 Extreme points; 0.10 Various tools; 1 Ideal norms and operator ideals; 1.1 Ideal norms; 1.2 Operator ideals; 1.3 Classes of Banach spaces; 2 Ideal norms associated with matrices; 2.1 Matrices; 2.2 Parseval ideal norms and 2-summing operators | |
| 505 | 8 | |a 2.3 Kwapien ideal norms and Hilbertian operators2.4 Ideal norms associated with Hilbert matrices; 3 Ideal norms associated with orthonormal systems; 3.1 Orthonormal systems; 3.2 Khintchine constants; 3.3 Riemann ideal norms; 3.4 Dirichlet ideal norms; 3.5 Orthonormal systems with special properties; 3.6 Tensor products of orthonormal systems; 3.7 Type and cotype ideal norms; 3.8 Characters on compact Abelian groups; 3.9 Discrete orthonormal systems; 3.10 Some universal ideal norms; 3.11 Parseval ideal norms; 4 Rademacher and Gauss ideal norms; 4.1 Rademacher functions | |
| 505 | 8 | |a 4.2 Rademacher type and cotype ideal norms4.3 Operators of Rademacher type; 4.4 B-convexity; 4.5 Operators of Rademacher cotype; 4.6 MP-convexity; 4.7 Gaussian random variables; 4.8 Gauss versus Rademacher; 4.9 Gauss type and cotype ideal norms; 4.10 Operators of Gauss type and cotype; 4.11 Sidon constants; 4.12 The Dirichlet ideal norms 6(#n, ftn) and 6(Sn, Sn); 4.13 Inequalities between 6(Rn, Rn) and g(R,n,J n); 4.14 The vector-valued Rademacher projection; 4.15 Parseval ideal norms and 7-summing operators; 4.16 The Maurey-Pisier theorem; 5 Trigonometric ideal norms | |
| 505 | 8 | |a 5.1 Trigonometric functions5.2 The Dirichlet ideal norms 6(£n, £n); 5.3 Hilbert matrices and trigonometric systems; 5.4 The vector-valued Hilbert transform; 5.5 Fourier type and cotype ideal norms; 5.6 Operators of Fourier type; 5.7 Operators of Fourier cotype; 5.8 The vector-valued Fourier transform; 5.9 Fourier versus Gauss and Rademacher; 6 Walsh ideal norms; 6.1 Walsh functions; 6.2 Walsh type and cotype ideal norms; 6.3 Operators of Walsh type; 6.4 Walsh versus Rademacher; 6.5 Walsh versus Fourier; 7 Haar ideal norms; 7.1 Martingales; 7.2 Dyadic martingales; 7.3 Haar functions | |
| 505 | 8 | |a 7.4 Haar type and cotype ideal norms7.5 Operators of Haar type; 7.6 Super weakly compact operators; 7.7 Martingale type ideal norms; 7.8 J-convexity; 7.9 Uniform g-convexity and uniform p-smoothness; 7.10 Uniform convexity and uniform smoothness; 8 Unconditionality; 8.1 Unconditional Riemann ideal norms; 8.2 Unconditional Dirichlet ideal norms; 8.3 Random unconditionality; 8.4 Fourier unconditionality; 8.5 Haar unconditionality/UMD; 8.6 Random Haar unconditionality; 8.7 The Dirichlet ideal norms (Wn, Wn); 8.8 The Burkholder-Bourgain theorem; 9 Miscellaneous; 9.1 Interpolation | |
| 650 | 0 | |a Banach spaces. |0 http://id.loc.gov/authorities/subjects/sh85011441 | |
| 650 | 0 | |a Mathematical analysis. |0 http://id.loc.gov/authorities/subjects/sh85082116 | |
| 650 | 6 | |a Espaces de Banach. | |
| 650 | 6 | |a Analyse mathématique. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Banach spaces |2 fast | |
| 650 | 7 | |a Mathematical analysis |2 fast | |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn708568563 |
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| _version_ | 1816881754417397760 |
| adam_text | |
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| author | Pietsch, A. (Albrecht) |
| author2 | Wenzel, Jörg |
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| author_GND | http://id.loc.gov/authorities/names/n79006402 http://id.loc.gov/authorities/names/nb98043315 |
| author_facet | Pietsch, A. (Albrecht) Wenzel, Jörg |
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| callnumber-first | Q - Science |
| callnumber-label | QA322 |
| callnumber-raw | QA322.2 .P54 1998eb |
| callnumber-search | QA322.2 .P54 1998eb |
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| collection | ZDB-4-EBA |
| contents | Cover; Half-title; Title; Copyright; Contents; Preface; Introduction; 0 Preliminaries; 0.1 Banach spaces and operators; 0.2 Finite dimensional spaces and operators; 0.3 Classical sequence spaces; 0.4 Classical function spaces; 0.5 Lorentz spaces; 0.6 Interpolation methods; 0.7 Summation operators; 0.8 Finite representability and ultrapowers; 0.9 Extreme points; 0.10 Various tools; 1 Ideal norms and operator ideals; 1.1 Ideal norms; 1.2 Operator ideals; 1.3 Classes of Banach spaces; 2 Ideal norms associated with matrices; 2.1 Matrices; 2.2 Parseval ideal norms and 2-summing operators 2.3 Kwapien ideal norms and Hilbertian operators2.4 Ideal norms associated with Hilbert matrices; 3 Ideal norms associated with orthonormal systems; 3.1 Orthonormal systems; 3.2 Khintchine constants; 3.3 Riemann ideal norms; 3.4 Dirichlet ideal norms; 3.5 Orthonormal systems with special properties; 3.6 Tensor products of orthonormal systems; 3.7 Type and cotype ideal norms; 3.8 Characters on compact Abelian groups; 3.9 Discrete orthonormal systems; 3.10 Some universal ideal norms; 3.11 Parseval ideal norms; 4 Rademacher and Gauss ideal norms; 4.1 Rademacher functions 4.2 Rademacher type and cotype ideal norms4.3 Operators of Rademacher type; 4.4 B-convexity; 4.5 Operators of Rademacher cotype; 4.6 MP-convexity; 4.7 Gaussian random variables; 4.8 Gauss versus Rademacher; 4.9 Gauss type and cotype ideal norms; 4.10 Operators of Gauss type and cotype; 4.11 Sidon constants; 4.12 The Dirichlet ideal norms 6(#n, ftn) and 6(Sn, Sn); 4.13 Inequalities between 6(Rn, Rn) and g(R,n,J n); 4.14 The vector-valued Rademacher projection; 4.15 Parseval ideal norms and 7-summing operators; 4.16 The Maurey-Pisier theorem; 5 Trigonometric ideal norms 5.1 Trigonometric functions5.2 The Dirichlet ideal norms 6(£n, £n); 5.3 Hilbert matrices and trigonometric systems; 5.4 The vector-valued Hilbert transform; 5.5 Fourier type and cotype ideal norms; 5.6 Operators of Fourier type; 5.7 Operators of Fourier cotype; 5.8 The vector-valued Fourier transform; 5.9 Fourier versus Gauss and Rademacher; 6 Walsh ideal norms; 6.1 Walsh functions; 6.2 Walsh type and cotype ideal norms; 6.3 Operators of Walsh type; 6.4 Walsh versus Rademacher; 6.5 Walsh versus Fourier; 7 Haar ideal norms; 7.1 Martingales; 7.2 Dyadic martingales; 7.3 Haar functions 7.4 Haar type and cotype ideal norms7.5 Operators of Haar type; 7.6 Super weakly compact operators; 7.7 Martingale type ideal norms; 7.8 J-convexity; 7.9 Uniform g-convexity and uniform p-smoothness; 7.10 Uniform convexity and uniform smoothness; 8 Unconditionality; 8.1 Unconditional Riemann ideal norms; 8.2 Unconditional Dirichlet ideal norms; 8.3 Random unconditionality; 8.4 Fourier unconditionality; 8.5 Haar unconditionality/UMD; 8.6 Random Haar unconditionality; 8.7 The Dirichlet ideal norms (Wn, Wn); 8.8 The Burkholder-Bourgain theorem; 9 Miscellaneous; 9.1 Interpolation |
| ctrlnum | (OCoLC)708568563 |
| dewey-full | 515/.732 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.732 |
| dewey-search | 515/.732 |
| dewey-sort | 3515 3732 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn708568563 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:17:45Z |
| institution | BVB |
| isbn | 9781107089105 1107089107 9780511526145 0511526148 |
| language | English |
| oclc_num | 708568563 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (ix, 553 pages) : illustrations. |
| psigel | ZDB-4-EBA |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications ; |
| series2 | Encyclopedia of mathematics and its applications ; |
| spelling | Pietsch, A. (Albrecht) https://id.oclc.org/worldcat/entity/E39PBJht7XytvdhXrTkp3RMkjC http://id.loc.gov/authorities/names/n79006402 Orthonormal systems and Banach space geometry / Albrecht Pietsch & Jörg Wenzel. Cambridge : Cambridge University Press, ©1998. 1 online resource (ix, 553 pages) : illustrations. text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of mathematics and its applications ; v. 70 Includes bibliographical references (pages 523-545) and index. Print version record. Orthonormal Systems and Banach Space Geometry describes the interplay between orthonormal expansions and Banach space geometry. Using harmonic analysis as a starting platform, classical inequalities and special functions are used to study orthonormal systems leading to an understanding of the advantages of systems consisting of characters on compact Abelian groups. Probabilistic concepts such as random variables and martingales are employed and Ramsey's theorem is used to study the theory of super-reflexivity. The text yields a detailed insight into concepts including type and co-type of Banach spaces, B-convexity, super-reflexivity, the vector-valued Fourier transform, the vector-valued Hilbert transform and the unconditionality property for martingale differences (UMD). A long list of unsolved problems is included as a starting point for research. This book should be accessible to graduate students and researchers with some basic knowledge of Banach space theory, real analysis, probability and algebra. Cover; Half-title; Title; Copyright; Contents; Preface; Introduction; 0 Preliminaries; 0.1 Banach spaces and operators; 0.2 Finite dimensional spaces and operators; 0.3 Classical sequence spaces; 0.4 Classical function spaces; 0.5 Lorentz spaces; 0.6 Interpolation methods; 0.7 Summation operators; 0.8 Finite representability and ultrapowers; 0.9 Extreme points; 0.10 Various tools; 1 Ideal norms and operator ideals; 1.1 Ideal norms; 1.2 Operator ideals; 1.3 Classes of Banach spaces; 2 Ideal norms associated with matrices; 2.1 Matrices; 2.2 Parseval ideal norms and 2-summing operators 2.3 Kwapien ideal norms and Hilbertian operators2.4 Ideal norms associated with Hilbert matrices; 3 Ideal norms associated with orthonormal systems; 3.1 Orthonormal systems; 3.2 Khintchine constants; 3.3 Riemann ideal norms; 3.4 Dirichlet ideal norms; 3.5 Orthonormal systems with special properties; 3.6 Tensor products of orthonormal systems; 3.7 Type and cotype ideal norms; 3.8 Characters on compact Abelian groups; 3.9 Discrete orthonormal systems; 3.10 Some universal ideal norms; 3.11 Parseval ideal norms; 4 Rademacher and Gauss ideal norms; 4.1 Rademacher functions 4.2 Rademacher type and cotype ideal norms4.3 Operators of Rademacher type; 4.4 B-convexity; 4.5 Operators of Rademacher cotype; 4.6 MP-convexity; 4.7 Gaussian random variables; 4.8 Gauss versus Rademacher; 4.9 Gauss type and cotype ideal norms; 4.10 Operators of Gauss type and cotype; 4.11 Sidon constants; 4.12 The Dirichlet ideal norms 6(#n, ftn) and 6(Sn, Sn); 4.13 Inequalities between 6(Rn, Rn) and g(R,n,J n); 4.14 The vector-valued Rademacher projection; 4.15 Parseval ideal norms and 7-summing operators; 4.16 The Maurey-Pisier theorem; 5 Trigonometric ideal norms 5.1 Trigonometric functions5.2 The Dirichlet ideal norms 6(£n, £n); 5.3 Hilbert matrices and trigonometric systems; 5.4 The vector-valued Hilbert transform; 5.5 Fourier type and cotype ideal norms; 5.6 Operators of Fourier type; 5.7 Operators of Fourier cotype; 5.8 The vector-valued Fourier transform; 5.9 Fourier versus Gauss and Rademacher; 6 Walsh ideal norms; 6.1 Walsh functions; 6.2 Walsh type and cotype ideal norms; 6.3 Operators of Walsh type; 6.4 Walsh versus Rademacher; 6.5 Walsh versus Fourier; 7 Haar ideal norms; 7.1 Martingales; 7.2 Dyadic martingales; 7.3 Haar functions 7.4 Haar type and cotype ideal norms7.5 Operators of Haar type; 7.6 Super weakly compact operators; 7.7 Martingale type ideal norms; 7.8 J-convexity; 7.9 Uniform g-convexity and uniform p-smoothness; 7.10 Uniform convexity and uniform smoothness; 8 Unconditionality; 8.1 Unconditional Riemann ideal norms; 8.2 Unconditional Dirichlet ideal norms; 8.3 Random unconditionality; 8.4 Fourier unconditionality; 8.5 Haar unconditionality/UMD; 8.6 Random Haar unconditionality; 8.7 The Dirichlet ideal norms (Wn, Wn); 8.8 The Burkholder-Bourgain theorem; 9 Miscellaneous; 9.1 Interpolation Banach spaces. http://id.loc.gov/authorities/subjects/sh85011441 Mathematical analysis. http://id.loc.gov/authorities/subjects/sh85082116 Espaces de Banach. Analyse mathématique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Banach spaces fast Mathematical analysis fast Wenzel, Jörg. http://id.loc.gov/authorities/names/nb98043315 Original 0521624622 9780521624626 (DLC) 98227912 Encyclopedia of mathematics and its applications ; v. 70. http://id.loc.gov/authorities/names/n42010632 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569301 Volltext |
| spellingShingle | Pietsch, A. (Albrecht) Orthonormal systems and Banach space geometry / Encyclopedia of mathematics and its applications ; Cover; Half-title; Title; Copyright; Contents; Preface; Introduction; 0 Preliminaries; 0.1 Banach spaces and operators; 0.2 Finite dimensional spaces and operators; 0.3 Classical sequence spaces; 0.4 Classical function spaces; 0.5 Lorentz spaces; 0.6 Interpolation methods; 0.7 Summation operators; 0.8 Finite representability and ultrapowers; 0.9 Extreme points; 0.10 Various tools; 1 Ideal norms and operator ideals; 1.1 Ideal norms; 1.2 Operator ideals; 1.3 Classes of Banach spaces; 2 Ideal norms associated with matrices; 2.1 Matrices; 2.2 Parseval ideal norms and 2-summing operators 2.3 Kwapien ideal norms and Hilbertian operators2.4 Ideal norms associated with Hilbert matrices; 3 Ideal norms associated with orthonormal systems; 3.1 Orthonormal systems; 3.2 Khintchine constants; 3.3 Riemann ideal norms; 3.4 Dirichlet ideal norms; 3.5 Orthonormal systems with special properties; 3.6 Tensor products of orthonormal systems; 3.7 Type and cotype ideal norms; 3.8 Characters on compact Abelian groups; 3.9 Discrete orthonormal systems; 3.10 Some universal ideal norms; 3.11 Parseval ideal norms; 4 Rademacher and Gauss ideal norms; 4.1 Rademacher functions 4.2 Rademacher type and cotype ideal norms4.3 Operators of Rademacher type; 4.4 B-convexity; 4.5 Operators of Rademacher cotype; 4.6 MP-convexity; 4.7 Gaussian random variables; 4.8 Gauss versus Rademacher; 4.9 Gauss type and cotype ideal norms; 4.10 Operators of Gauss type and cotype; 4.11 Sidon constants; 4.12 The Dirichlet ideal norms 6(#n, ftn) and 6(Sn, Sn); 4.13 Inequalities between 6(Rn, Rn) and g(R,n,J n); 4.14 The vector-valued Rademacher projection; 4.15 Parseval ideal norms and 7-summing operators; 4.16 The Maurey-Pisier theorem; 5 Trigonometric ideal norms 5.1 Trigonometric functions5.2 The Dirichlet ideal norms 6(£n, £n); 5.3 Hilbert matrices and trigonometric systems; 5.4 The vector-valued Hilbert transform; 5.5 Fourier type and cotype ideal norms; 5.6 Operators of Fourier type; 5.7 Operators of Fourier cotype; 5.8 The vector-valued Fourier transform; 5.9 Fourier versus Gauss and Rademacher; 6 Walsh ideal norms; 6.1 Walsh functions; 6.2 Walsh type and cotype ideal norms; 6.3 Operators of Walsh type; 6.4 Walsh versus Rademacher; 6.5 Walsh versus Fourier; 7 Haar ideal norms; 7.1 Martingales; 7.2 Dyadic martingales; 7.3 Haar functions 7.4 Haar type and cotype ideal norms7.5 Operators of Haar type; 7.6 Super weakly compact operators; 7.7 Martingale type ideal norms; 7.8 J-convexity; 7.9 Uniform g-convexity and uniform p-smoothness; 7.10 Uniform convexity and uniform smoothness; 8 Unconditionality; 8.1 Unconditional Riemann ideal norms; 8.2 Unconditional Dirichlet ideal norms; 8.3 Random unconditionality; 8.4 Fourier unconditionality; 8.5 Haar unconditionality/UMD; 8.6 Random Haar unconditionality; 8.7 The Dirichlet ideal norms (Wn, Wn); 8.8 The Burkholder-Bourgain theorem; 9 Miscellaneous; 9.1 Interpolation Banach spaces. http://id.loc.gov/authorities/subjects/sh85011441 Mathematical analysis. http://id.loc.gov/authorities/subjects/sh85082116 Espaces de Banach. Analyse mathématique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Banach spaces fast Mathematical analysis fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85011441 http://id.loc.gov/authorities/subjects/sh85082116 |
| title | Orthonormal systems and Banach space geometry / |
| title_auth | Orthonormal systems and Banach space geometry / |
| title_exact_search | Orthonormal systems and Banach space geometry / |
| title_full | Orthonormal systems and Banach space geometry / Albrecht Pietsch & Jörg Wenzel. |
| title_fullStr | Orthonormal systems and Banach space geometry / Albrecht Pietsch & Jörg Wenzel. |
| title_full_unstemmed | Orthonormal systems and Banach space geometry / Albrecht Pietsch & Jörg Wenzel. |
| title_short | Orthonormal systems and Banach space geometry / |
| title_sort | orthonormal systems and banach space geometry |
| topic | Banach spaces. http://id.loc.gov/authorities/subjects/sh85011441 Mathematical analysis. http://id.loc.gov/authorities/subjects/sh85082116 Espaces de Banach. Analyse mathématique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Banach spaces fast Mathematical analysis fast |
| topic_facet | Banach spaces. Mathematical analysis. Espaces de Banach. Analyse mathématique. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Banach spaces Mathematical analysis |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569301 |
| work_keys_str_mv | AT pietscha orthonormalsystemsandbanachspacegeometry AT wenzeljorg orthonormalsystemsandbanachspacegeometry |