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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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c2009
|
| Schriftenreihe: | Series on concrete and applicable mathematics
v. 8 |
| Schlagworte: | |
| Online-Zugang: | FHN01 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-Szasz-Mirakjan, Baskakov and Balazs-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 Vallee Poussin, Fejer, 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: | xii, 337 p |
| ISBN: | 9789814282437 |
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| 490 | 0 | |a Series on concrete and applicable mathematics |v v. 8 | |
| 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-Szasz-Mirakjan, Baskakov and Balazs-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 Vallee Poussin, Fejer, 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 | ||
| 650 | 4 | |a Approximation theory | |
| 650 | 4 | |a Operator theory | |
| 650 | 4 | |a Bernstein polynomials | |
| 650 | 4 | |a Convolutions (Mathematics) | |
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Datensatz im Suchindex
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| author | Gal, Sorin G. 1953- |
| author_facet | Gal, Sorin G. 1953- |
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| author_sort | Gal, Sorin G. 1953- |
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| dewey-full | 511.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| 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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| id | DE-604.BV044637834 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:52Z |
| institution | BVB |
| isbn | 9789814282437 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030035807 |
| oclc_num | 1012628467 |
| open_access_boolean | |
| owner | DE-92 |
| owner_facet | DE-92 |
| physical | xii, 337 p |
| psigel | ZDB-124-WOP ZDB-124-WOP FHN_PDA_WOP |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | World Scientific Pub. Co. |
| record_format | marc |
| series2 | Series on concrete and applicable mathematics |
| spelling | Gal, Sorin G. 1953- Verfasser aut Approximation by complex Bernstein and convolution type operators Sorin G. Gal Singapore World Scientific Pub. Co. c2009 xii, 337 p txt rdacontent c rdamedia cr rdacarrier Series on concrete and applicable mathematics v. 8 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-Szasz-Mirakjan, Baskakov and Balazs-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 Vallee Poussin, Fejer, 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 Approximation theory Operator theory Bernstein polynomials Convolutions (Mathematics) Erscheint auch als Druck-Ausgabe 9789814282420 Erscheint auch als Druck-Ausgabe 9814282421 http://www.worldscientific.com/worldscibooks/10.1142/7426#t=toc Verlag URL des Erstveroeffentlichers Volltext |
| spellingShingle | Gal, Sorin G. 1953- Approximation by complex Bernstein and convolution type operators Approximation theory Operator theory Bernstein polynomials Convolutions (Mathematics) |
| 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 Operator theory Bernstein polynomials Convolutions (Mathematics) |
| topic_facet | Approximation theory Operator theory Bernstein polynomials Convolutions (Mathematics) |
| url | http://www.worldscientific.com/worldscibooks/10.1142/7426#t=toc |
| work_keys_str_mv | AT galsoring approximationbycomplexbernsteinandconvolutiontypeoperators |