Analysis in positive characteristic:
Devoted to counterparts of classical structures of mathematical analysis in analysis over local fields of positive characteristic, this book treats positive characteristic phenomena from an analytic viewpoint. Building on the basic objects introduced by L. Carlitz - such as the Carlitz factorials, e...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2009
|
| Series: | Cambridge tracts in mathematics
178 |
| Subjects: | |
| Online Access: | DE-12 DE-92 DE-355 Volltext |
| Summary: | Devoted to counterparts of classical structures of mathematical analysis in analysis over local fields of positive characteristic, this book treats positive characteristic phenomena from an analytic viewpoint. Building on the basic objects introduced by L. Carlitz - such as the Carlitz factorials, exponential and logarithm, and the orthonormal system of Carlitz polynomials - the author develops a kind of differential and integral calculi. He also expands on the basics of an analytic theory of (Carlitz's) differential equations, providing a useful foundation for the study of various special functions. The differential calculus is extended to a type of Rota's umbral calculus, and an investigation is made of the corresponding rings of differential operators. A theory of quasi-holonomic modules over these rings, having some common features with holonomic modules in the sense of Bernstein, is also connected to some special functions in the spirit of Zeilberger's theory |
| Physical Description: | 1 Online-Ressource (ix, 210 Seiten) |
| ISBN: | 9780511575624 |
| DOI: | 10.1017/CBO9780511575624 |
Staff View
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| contents | Orthonormal systems and their applications -- Calculus -- Differential equations -- Special functions -- The Carlitz rings |
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| id | DE-604.BV043942238 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-03T00:35:41Z |
| institution | BVB |
| isbn | 9780511575624 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351207 |
| oclc_num | 850997012 |
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| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (ix, 210 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge tracts in mathematics |
| spelling | Kočubej, Anatolij Naumovyč 1949- Verfasser (DE-588)133201651 aut Analysis in positive characteristic Anatoly N. Kochubei Cambridge Cambridge University Press 2009 1 Online-Ressource (ix, 210 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 178 Orthonormal systems and their applications -- Calculus -- Differential equations -- Special functions -- The Carlitz rings Devoted to counterparts of classical structures of mathematical analysis in analysis over local fields of positive characteristic, this book treats positive characteristic phenomena from an analytic viewpoint. Building on the basic objects introduced by L. Carlitz - such as the Carlitz factorials, exponential and logarithm, and the orthonormal system of Carlitz polynomials - the author develops a kind of differential and integral calculi. He also expands on the basics of an analytic theory of (Carlitz's) differential equations, providing a useful foundation for the study of various special functions. The differential calculus is extended to a type of Rota's umbral calculus, and an investigation is made of the corresponding rings of differential operators. A theory of quasi-holonomic modules over these rings, having some common features with holonomic modules in the sense of Bernstein, is also connected to some special functions in the spirit of Zeilberger's theory Mathematical analysis Local fields (Algebra) Lokaler Körper (DE-588)4266744-6 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Positive Charakteristik (DE-588)4472919-4 gnd rswk-swf Lokaler Körper (DE-588)4266744-6 s Positive Charakteristik (DE-588)4472919-4 s Analysis (DE-588)4001865-9 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-50977-0 https://doi.org/10.1017/CBO9780511575624 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Kočubej, Anatolij Naumovyč 1949- Analysis in positive characteristic Orthonormal systems and their applications -- Calculus -- Differential equations -- Special functions -- The Carlitz rings Mathematical analysis Local fields (Algebra) Lokaler Körper (DE-588)4266744-6 gnd Analysis (DE-588)4001865-9 gnd Positive Charakteristik (DE-588)4472919-4 gnd |
| subject_GND | (DE-588)4266744-6 (DE-588)4001865-9 (DE-588)4472919-4 |
| title | Analysis in positive characteristic |
| title_auth | Analysis in positive characteristic |
| title_exact_search | Analysis in positive characteristic |
| title_full | Analysis in positive characteristic Anatoly N. Kochubei |
| title_fullStr | Analysis in positive characteristic Anatoly N. Kochubei |
| title_full_unstemmed | Analysis in positive characteristic Anatoly N. Kochubei |
| title_short | Analysis in positive characteristic |
| title_sort | analysis in positive characteristic |
| topic | Mathematical analysis Local fields (Algebra) Lokaler Körper (DE-588)4266744-6 gnd Analysis (DE-588)4001865-9 gnd Positive Charakteristik (DE-588)4472919-4 gnd |
| topic_facet | Mathematical analysis Local fields (Algebra) Lokaler Körper Analysis Positive Charakteristik |
| url | https://doi.org/10.1017/CBO9780511575624 |
| work_keys_str_mv | AT kocubejanatolijnaumovyc analysisinpositivecharacteristic |