Polynomial expansions of analytic functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1964
|
| Ausgabe: | Second Printing Corrected |
| Schriftenreihe: | Ergebnisse der Mathematik und Ihrer Grenzgebiete : Neue Folge
19 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This monograph deals with the expansion properties, in the complex domain, of sets of polynomials which are defined by generating relations. It thus represents a synthesis of two branches of analysis which have been developing almost independently. On the one hand there has grown up a body of results dealing with the more or less formal properties of sets of polynomials which possess simple generating relations. Much of this material is summarized in the Bateman compendia (ERDELYI [1], voi. III, chap. 19) and in TRUESDELL [1]. On the other hand, a problem of fundamental interest in classical analysis is to study the representability of an analytic function f(z) as a series ,Lc,. p,. (z), where {p,. } is a prescribed sequence of functions, and the connections between the function f and the coefficients c,. . BIEBERBACH's monograph Analytische Fortsetzung (Ergebnisse der Mathematik, new series, no. 3) can be regarded as a study of this problem for the special choice p,. (z) =z", and illustrates the depth and detail which such a specialization allows. However, the wealth of available information about other sets of polynomials has seldom been put to work in this connection (the application of generating relations to expansion of functions is not even mentioned in the Bateman compendia). At the other extreme, J. M. |
| Beschreibung: | 1 Online-Ressource (VIII, 77 p) |
| ISBN: | 9783662251706 9783662231791 |
| DOI: | 10.1007/978-3-662-25170-6 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804153099336548352 |
|---|---|
| any_adam_object | |
| author | Boas, Ralph P. |
| author_facet | Boas, Ralph P. |
| author_role | aut |
| author_sort | Boas, Ralph P. |
| author_variant | r p b rp rpb |
| building | Verbundindex |
| bvnumber | BV042423517 |
| classification_tum | MAT 000 |
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| dewey-full | 515.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7 |
| dewey-search | 515.7 |
| dewey-sort | 3515.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-25170-6 |
| edition | Second Printing Corrected |
| format | Electronic eBook |
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| id | DE-604.BV042423517 |
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| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662251706 9783662231791 |
| language | English |
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| series2 | Ergebnisse der Mathematik und Ihrer Grenzgebiete : Neue Folge |
| spelling | Boas, Ralph P. Verfasser aut Polynomial expansions of analytic functions by Ralph P. Boas, R. Creighton Buck Second Printing Corrected Berlin, Heidelberg Springer Berlin Heidelberg 1964 1 Online-Ressource (VIII, 77 p) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und Ihrer Grenzgebiete : Neue Folge 19 This monograph deals with the expansion properties, in the complex domain, of sets of polynomials which are defined by generating relations. It thus represents a synthesis of two branches of analysis which have been developing almost independently. On the one hand there has grown up a body of results dealing with the more or less formal properties of sets of polynomials which possess simple generating relations. Much of this material is summarized in the Bateman compendia (ERDELYI [1], voi. III, chap. 19) and in TRUESDELL [1]. On the other hand, a problem of fundamental interest in classical analysis is to study the representability of an analytic function f(z) as a series ,Lc,. p,. (z), where {p,. } is a prescribed sequence of functions, and the connections between the function f and the coefficients c,. . BIEBERBACH's monograph Analytische Fortsetzung (Ergebnisse der Mathematik, new series, no. 3) can be regarded as a study of this problem for the special choice p,. (z) =z", and illustrates the depth and detail which such a specialization allows. However, the wealth of available information about other sets of polynomials has seldom been put to work in this connection (the application of generating relations to expansion of functions is not even mentioned in the Bateman compendia). At the other extreme, J. M. Mathematics Global analysis (Mathematics) Functional analysis Functional Analysis Analysis Mathematik Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Polynomerweiterung (DE-588)4175261-2 gnd rswk-swf Analytische Funktion (DE-588)4142348-3 gnd rswk-swf Polynom (DE-588)4046711-9 gnd rswk-swf Holomorphe Funktion (DE-588)4025645-5 gnd rswk-swf Analytische Funktion (DE-588)4142348-3 s Polynom (DE-588)4046711-9 s 1\p DE-604 Polynomerweiterung (DE-588)4175261-2 s 2\p DE-604 Holomorphe Funktion (DE-588)4025645-5 s 3\p DE-604 Approximationstheorie (DE-588)4120913-8 s 4\p DE-604 Buck, R. Creighton Sonstige oth Ergebnisse der Mathematik und Ihrer Grenzgebiete Neue Folge 19 (DE-604)BV005871160 19 https://doi.org/10.1007/978-3-662-25170-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Boas, Ralph P. Polynomial expansions of analytic functions Mathematics Global analysis (Mathematics) Functional analysis Functional Analysis Analysis Mathematik Approximationstheorie (DE-588)4120913-8 gnd Polynomerweiterung (DE-588)4175261-2 gnd Analytische Funktion (DE-588)4142348-3 gnd Polynom (DE-588)4046711-9 gnd Holomorphe Funktion (DE-588)4025645-5 gnd |
| subject_GND | (DE-588)4120913-8 (DE-588)4175261-2 (DE-588)4142348-3 (DE-588)4046711-9 (DE-588)4025645-5 |
| title | Polynomial expansions of analytic functions |
| title_auth | Polynomial expansions of analytic functions |
| title_exact_search | Polynomial expansions of analytic functions |
| title_full | Polynomial expansions of analytic functions by Ralph P. Boas, R. Creighton Buck |
| title_fullStr | Polynomial expansions of analytic functions by Ralph P. Boas, R. Creighton Buck |
| title_full_unstemmed | Polynomial expansions of analytic functions by Ralph P. Boas, R. Creighton Buck |
| title_short | Polynomial expansions of analytic functions |
| title_sort | polynomial expansions of analytic functions |
| topic | Mathematics Global analysis (Mathematics) Functional analysis Functional Analysis Analysis Mathematik Approximationstheorie (DE-588)4120913-8 gnd Polynomerweiterung (DE-588)4175261-2 gnd Analytische Funktion (DE-588)4142348-3 gnd Polynom (DE-588)4046711-9 gnd Holomorphe Funktion (DE-588)4025645-5 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Functional analysis Functional Analysis Analysis Mathematik Approximationstheorie Polynomerweiterung Analytische Funktion Polynom Holomorphe Funktion |
| url | https://doi.org/10.1007/978-3-662-25170-6 |
| volume_link | (DE-604)BV005871160 |
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