Generalized Functions, Volume 6
Representation Theory and Automorphic Functions
Seiten
2025
American Mathematical Society (Verlag)
978-1-4704-8115-5 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-8115-5 (ISBN)
Delving into the theory of generalized functions, the text illuminates their role in analysis, partial differential equations, stochastic processes, and representation theory. It probes representations of the general linear group over p-adic fields, power series fields, and adeles, unveiling links to automorphic functions.
The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, Generalized Functions, written by I. M. Gel'fand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. The unifying theme of Volume 6 is the study of representations of the general linear group of order two over various fields and rings of number-theoretic nature, most importantly over local fields ($p$-adic fields and fields of power series over finite fields) and over the ring of adeles. Representation theory of the latter group naturally leads to the study of automorphic functions and related number-theoretic problems. The book contains a wealth of information about discrete subgroups and automorphic representations, and can be used both as a very good introduction to the subject and as a valuable reference.
The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, Generalized Functions, written by I. M. Gel'fand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. The unifying theme of Volume 6 is the study of representations of the general linear group of order two over various fields and rings of number-theoretic nature, most importantly over local fields ($p$-adic fields and fields of power series over finite fields) and over the ring of adeles. Representation theory of the latter group naturally leads to the study of automorphic functions and related number-theoretic problems. The book contains a wealth of information about discrete subgroups and automorphic representations, and can be used both as a very good introduction to the subject and as a valuable reference.
Chapters
Chapter 1. Homogeneous spaces with a discrete stability group
Chapter 2. Representations of the group of unimodular matrices of order 2 with elements from a locally compact topological field
Chapter 3. Representations of adele groups
Guide to the literature
| Erscheinungsdatum | 02.08.2025 |
|---|---|
| Reihe/Serie | AMS Chelsea Publishing |
| Verlagsort | Providence |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-4704-8115-4 / 1470481154 |
| ISBN-13 | 978-1-4704-8115-5 / 9781470481155 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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