Approximation by complex Bernstein and convolution type operators /:
The monograph, as its first main goal, aims to study the overconvergence phenomenon of important classes of Bernstein-type operators of one or several complex variables, that is, to extend their quantitative convergence properties to larger sets in the complex plane rather than the real intervals. T...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; Hackensack, N.J. :
World Scientific Pub. Co.,
©2009.
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| Schriftenreihe: | Series on concrete and applicable mathematics ;
v. 8. |
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| Online-Zugang: | Volltext |
| Zusammenfassung: | The monograph, as its first main goal, aims to study the overconvergence phenomenon of important classes of Bernstein-type operators of one or several complex variables, that is, to extend their quantitative convergence properties to larger sets in the complex plane rather than the real intervals. The operators studied are of the following types : Bernstein, Bernstein-Faber, Bernstein-Butzer, q-Bernstein, Bernstein-Stancu, Bernstein-Kantorovich, Favard-Szász-Mirakjan, Baskakov and Balázs-Szabados. The second main objective is to provide a study of the approximation and geometric properties of several types of complex convolutions : the de la Vallée Poussin, Fejér, Riesz-Zygmund, Jackson, Rogosinski, Picard, Poisson-Cauchy, Gauss-Weierstrass, q-Picard, q-Gauss-Weierstrass, Post-Widder, rotation-invariant, Sikkema and nonlinear. Several applications to partial differential equations (PDEs) are also presented. Many of the open problems encountered in the studies are proposed at the end of each chapter. For further research, the monograph suggests and advocates similar studies for other complex Bernstein-type operators, and for other linear and nonlinear convolutions. |
| Beschreibung: | 1 online resource (xii, 337 pages) |
| Format: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |
| Bibliographie: | Includes bibliographical references (pages 327-336) and index. |
| ISBN: | 9789814282437 981428243X |
| ISSN: | 1793-1142 ; |
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| 245 | 1 | 0 | |a Approximation by complex Bernstein and convolution type operators / |c Sorin G. Gal. |
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| 490 | 1 | |a Series on concrete and applicable mathematics, |x 1793-1142 ; |v v. 8 | |
| 504 | |a Includes bibliographical references (pages 327-336) and index. | ||
| 505 | 0 | |a 1. Bernstein-type operators of one complex variable. 1.0. Auxiliary results in complex analysis. 1.1. Berstein polynomials. 1.2. Iterates of Bernstein polynomials. 1.3. Generalized Voronovskaja theorems for Bernstein polynomials. 1.4. Butzer's linear combination of Bernstein polynomials. 1.5. q-Bernstein polynomials. 1.6. Bernstein-Stancu polynomials. 1.7. Bernstein-Kantorovich type polynomials. 1.8. Favard-Szász-Mirakjan operators. 1.9. Baskakov operators. 1.10. Balázs-Szabados operators. 1.11. Bibliographical notes and open problems -- 2. Bernstein-type operators of several complex variables. 2.1. Introduction. 2.2. Bernstein polynomials. 2.3. Favard-Szász-Mirakjan operators. 2.4. Baskakov operators. 2.5. Bibliographical notes and open problems -- 3. Complex convolutions. 3.1. Linear polynomial convolutions. 3.2. Linear non-polynomial convolutions. 3.3. Nonlinear complex convolutions. 3.4. Bibliographical notes and open problems. | |
| 520 | |a The monograph, as its first main goal, aims to study the overconvergence phenomenon of important classes of Bernstein-type operators of one or several complex variables, that is, to extend their quantitative convergence properties to larger sets in the complex plane rather than the real intervals. The operators studied are of the following types : Bernstein, Bernstein-Faber, Bernstein-Butzer, q-Bernstein, Bernstein-Stancu, Bernstein-Kantorovich, Favard-Szász-Mirakjan, Baskakov and Balázs-Szabados. The second main objective is to provide a study of the approximation and geometric properties of several types of complex convolutions : the de la Vallée Poussin, Fejér, Riesz-Zygmund, Jackson, Rogosinski, Picard, Poisson-Cauchy, Gauss-Weierstrass, q-Picard, q-Gauss-Weierstrass, Post-Widder, rotation-invariant, Sikkema and nonlinear. Several applications to partial differential equations (PDEs) are also presented. Many of the open problems encountered in the studies are proposed at the end of each chapter. For further research, the monograph suggests and advocates similar studies for other complex Bernstein-type operators, and for other linear and nonlinear convolutions. | ||
| 506 | |3 Use copy |f Restrictions unspecified |2 star |5 MiAaHDL | ||
| 533 | |a Electronic reproduction. |b [Place of publication not identified] : |c HathiTrust Digital Library, |d 2011. |5 MiAaHDL | ||
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| 650 | 0 | |a Convolutions (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85031752 | |
| 650 | 6 | |a Théorie de l'approximation. | |
| 650 | 6 | |a Théorie des opérateurs. | |
| 650 | 6 | |a Polynômes de Bernstein. | |
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| author | Gal, Sorin G., 1953- |
| author_GND | http://id.loc.gov/authorities/names/n99256513 |
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| contents | 1. Bernstein-type operators of one complex variable. 1.0. Auxiliary results in complex analysis. 1.1. Berstein polynomials. 1.2. Iterates of Bernstein polynomials. 1.3. Generalized Voronovskaja theorems for Bernstein polynomials. 1.4. Butzer's linear combination of Bernstein polynomials. 1.5. q-Bernstein polynomials. 1.6. Bernstein-Stancu polynomials. 1.7. Bernstein-Kantorovich type polynomials. 1.8. Favard-Szász-Mirakjan operators. 1.9. Baskakov operators. 1.10. Balázs-Szabados operators. 1.11. Bibliographical notes and open problems -- 2. Bernstein-type operators of several complex variables. 2.1. Introduction. 2.2. Bernstein polynomials. 2.3. Favard-Szász-Mirakjan operators. 2.4. Baskakov operators. 2.5. Bibliographical notes and open problems -- 3. Complex convolutions. 3.1. Linear polynomial convolutions. 3.2. Linear non-polynomial convolutions. 3.3. Nonlinear complex convolutions. 3.4. Bibliographical notes and open problems. |
| ctrlnum | (OCoLC)612412955 |
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| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.4 |
| dewey-search | 511.4 |
| dewey-sort | 3511.4 |
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| discipline | Mathematik |
| format | Electronic eBook |
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Bernstein-type operators of one complex variable. 1.0. Auxiliary results in complex analysis. 1.1. Berstein polynomials. 1.2. Iterates of Bernstein polynomials. 1.3. Generalized Voronovskaja theorems for Bernstein polynomials. 1.4. Butzer's linear combination of Bernstein polynomials. 1.5. q-Bernstein polynomials. 1.6. Bernstein-Stancu polynomials. 1.7. Bernstein-Kantorovich type polynomials. 1.8. Favard-Szász-Mirakjan operators. 1.9. Baskakov operators. 1.10. Balázs-Szabados operators. 1.11. Bibliographical notes and open problems -- 2. Bernstein-type operators of several complex variables. 2.1. Introduction. 2.2. Bernstein polynomials. 2.3. Favard-Szász-Mirakjan operators. 2.4. Baskakov operators. 2.5. Bibliographical notes and open problems -- 3. Complex convolutions. 3.1. Linear polynomial convolutions. 3.2. Linear non-polynomial convolutions. 3.3. Nonlinear complex convolutions. 3.4. 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| indexdate | 2024-11-27T13:17:11Z |
| institution | BVB |
| institution_GND | http://id.loc.gov/authorities/names/no2001005546 |
| isbn | 9789814282437 981428243X |
| issn | 1793-1142 ; |
| language | English |
| oclc_num | 612412955 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xii, 337 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | World Scientific Pub. Co., |
| record_format | marc |
| series | Series on concrete and applicable mathematics ; |
| series2 | Series on concrete and applicable mathematics, |
| spelling | Gal, Sorin G., 1953- https://id.oclc.org/worldcat/entity/E39PCjxmpxDQH799yTC9rc6R8C http://id.loc.gov/authorities/names/n99256513 Approximation by complex Bernstein and convolution type operators / Sorin G. Gal. Singapore ; Hackensack, N.J. : World Scientific Pub. Co., ©2009. 1 online resource (xii, 337 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Series on concrete and applicable mathematics, 1793-1142 ; v. 8 Includes bibliographical references (pages 327-336) and index. 1. Bernstein-type operators of one complex variable. 1.0. Auxiliary results in complex analysis. 1.1. Berstein polynomials. 1.2. Iterates of Bernstein polynomials. 1.3. Generalized Voronovskaja theorems for Bernstein polynomials. 1.4. Butzer's linear combination of Bernstein polynomials. 1.5. q-Bernstein polynomials. 1.6. Bernstein-Stancu polynomials. 1.7. Bernstein-Kantorovich type polynomials. 1.8. Favard-Szász-Mirakjan operators. 1.9. Baskakov operators. 1.10. Balázs-Szabados operators. 1.11. Bibliographical notes and open problems -- 2. Bernstein-type operators of several complex variables. 2.1. Introduction. 2.2. Bernstein polynomials. 2.3. Favard-Szász-Mirakjan operators. 2.4. Baskakov operators. 2.5. Bibliographical notes and open problems -- 3. Complex convolutions. 3.1. Linear polynomial convolutions. 3.2. Linear non-polynomial convolutions. 3.3. Nonlinear complex convolutions. 3.4. Bibliographical notes and open problems. The monograph, as its first main goal, aims to study the overconvergence phenomenon of important classes of Bernstein-type operators of one or several complex variables, that is, to extend their quantitative convergence properties to larger sets in the complex plane rather than the real intervals. The operators studied are of the following types : Bernstein, Bernstein-Faber, Bernstein-Butzer, q-Bernstein, Bernstein-Stancu, Bernstein-Kantorovich, Favard-Szász-Mirakjan, Baskakov and Balázs-Szabados. The second main objective is to provide a study of the approximation and geometric properties of several types of complex convolutions : the de la Vallée Poussin, Fejér, Riesz-Zygmund, Jackson, Rogosinski, Picard, Poisson-Cauchy, Gauss-Weierstrass, q-Picard, q-Gauss-Weierstrass, Post-Widder, rotation-invariant, Sikkema and nonlinear. Several applications to partial differential equations (PDEs) are also presented. Many of the open problems encountered in the studies are proposed at the end of each chapter. For further research, the monograph suggests and advocates similar studies for other complex Bernstein-type operators, and for other linear and nonlinear convolutions. Use copy Restrictions unspecified star MiAaHDL Electronic reproduction. [Place of publication not identified] : HathiTrust Digital Library, 2011. MiAaHDL Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL digitized 2011 HathiTrust Digital Library committed to preserve pda MiAaHDL Print version record. Approximation theory. http://id.loc.gov/authorities/subjects/sh85006190 Operator theory. http://id.loc.gov/authorities/subjects/sh85095029 Bernstein polynomials. http://id.loc.gov/authorities/subjects/sh85013377 Convolutions (Mathematics) http://id.loc.gov/authorities/subjects/sh85031752 Théorie de l'approximation. Théorie des opérateurs. Polynômes de Bernstein. Convolutions (Mathématiques) MATHEMATICS General. bisacsh Approximation theory fast Bernstein polynomials fast Convolutions (Mathematics) fast Operator theory fast World Scientific (Firm) http://id.loc.gov/authorities/names/no2001005546 has work: Approximation by complex Bernstein and convolution type operators (Text) https://id.oclc.org/worldcat/entity/E39PCGpWG7CkjCfFCMRt9fj7gX https://id.oclc.org/worldcat/ontology/hasWork 9814282421 9789814282420 Series on concrete and applicable mathematics ; v. 8. http://id.loc.gov/authorities/names/no2001065027 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=340525 Volltext |
| spellingShingle | Gal, Sorin G., 1953- Approximation by complex Bernstein and convolution type operators / Series on concrete and applicable mathematics ; 1. Bernstein-type operators of one complex variable. 1.0. Auxiliary results in complex analysis. 1.1. Berstein polynomials. 1.2. Iterates of Bernstein polynomials. 1.3. Generalized Voronovskaja theorems for Bernstein polynomials. 1.4. Butzer's linear combination of Bernstein polynomials. 1.5. q-Bernstein polynomials. 1.6. Bernstein-Stancu polynomials. 1.7. Bernstein-Kantorovich type polynomials. 1.8. Favard-Szász-Mirakjan operators. 1.9. Baskakov operators. 1.10. Balázs-Szabados operators. 1.11. Bibliographical notes and open problems -- 2. Bernstein-type operators of several complex variables. 2.1. Introduction. 2.2. Bernstein polynomials. 2.3. Favard-Szász-Mirakjan operators. 2.4. Baskakov operators. 2.5. Bibliographical notes and open problems -- 3. Complex convolutions. 3.1. Linear polynomial convolutions. 3.2. Linear non-polynomial convolutions. 3.3. Nonlinear complex convolutions. 3.4. Bibliographical notes and open problems. Approximation theory. http://id.loc.gov/authorities/subjects/sh85006190 Operator theory. http://id.loc.gov/authorities/subjects/sh85095029 Bernstein polynomials. http://id.loc.gov/authorities/subjects/sh85013377 Convolutions (Mathematics) http://id.loc.gov/authorities/subjects/sh85031752 Théorie de l'approximation. Théorie des opérateurs. Polynômes de Bernstein. Convolutions (Mathématiques) MATHEMATICS General. bisacsh Approximation theory fast Bernstein polynomials fast Convolutions (Mathematics) fast Operator theory fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85006190 http://id.loc.gov/authorities/subjects/sh85095029 http://id.loc.gov/authorities/subjects/sh85013377 http://id.loc.gov/authorities/subjects/sh85031752 |
| title | Approximation by complex Bernstein and convolution type operators / |
| title_auth | Approximation by complex Bernstein and convolution type operators / |
| title_exact_search | Approximation by complex Bernstein and convolution type operators / |
| title_full | Approximation by complex Bernstein and convolution type operators / Sorin G. Gal. |
| title_fullStr | Approximation by complex Bernstein and convolution type operators / Sorin G. Gal. |
| title_full_unstemmed | Approximation by complex Bernstein and convolution type operators / Sorin G. Gal. |
| title_short | Approximation by complex Bernstein and convolution type operators / |
| title_sort | approximation by complex bernstein and convolution type operators |
| topic | Approximation theory. http://id.loc.gov/authorities/subjects/sh85006190 Operator theory. http://id.loc.gov/authorities/subjects/sh85095029 Bernstein polynomials. http://id.loc.gov/authorities/subjects/sh85013377 Convolutions (Mathematics) http://id.loc.gov/authorities/subjects/sh85031752 Théorie de l'approximation. Théorie des opérateurs. Polynômes de Bernstein. Convolutions (Mathématiques) MATHEMATICS General. bisacsh Approximation theory fast Bernstein polynomials fast Convolutions (Mathematics) fast Operator theory fast |
| topic_facet | Approximation theory. Operator theory. Bernstein polynomials. Convolutions (Mathematics) Théorie de l'approximation. Théorie des opérateurs. Polynômes de Bernstein. Convolutions (Mathématiques) MATHEMATICS General. Approximation theory Bernstein polynomials Operator theory |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=340525 |
| work_keys_str_mv | AT galsoring approximationbycomplexbernsteinandconvolutiontypeoperators AT worldscientificfirm approximationbycomplexbernsteinandconvolutiontypeoperators |