Generalized functions, volume 6 : representation theory and automorphic functions
Gelʹfand, I. M.
Generalized functions, volume 6 : representation theory and automorphic functions - Providence, Rhode Island : American Mathematical Society Chelsea Publishing, 2016. - xvi, 426p. : illustrations (black and white) ; 26 cm.
Includes bibliographical references and index.
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.
9781470426644 9781470428853
Theory of distributions (Functional analysis)
Functional analysis -- Distributions, generalized functions, distribution spaces -- Distributions, generalized functions, distribution spaces
Automorphic functions
Group theory
Representations of algebras
Representations of groups
Selberg trace formula
517.98 / GEL-G
Generalized functions, volume 6 : representation theory and automorphic functions - Providence, Rhode Island : American Mathematical Society Chelsea Publishing, 2016. - xvi, 426p. : illustrations (black and white) ; 26 cm.
Includes bibliographical references and index.
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.
9781470426644 9781470428853
Theory of distributions (Functional analysis)
Functional analysis -- Distributions, generalized functions, distribution spaces -- Distributions, generalized functions, distribution spaces
Automorphic functions
Group theory
Representations of algebras
Representations of groups
Selberg trace formula
517.98 / GEL-G
