Harmonic analysis on symmetric spaces -- higher rank spaces, positive definite matrix space and generalizations. (2016)

• Record Type: Book
• Uniform Title: Harmonic analysis on symmetric spaces and applications
• Further Information: Note: Audrey Terras.
• Authors: Terras, Audrey
• Contents: Intro; Preface to the First Edition; Preface to the Second Edition; Contents; List of Figures; 1 The Space Pn of Positive nn Matrices; 1.1 Geometry and Analysis on Pn; 1.1.1 Introduction; 1.1.2 Elementary Results; 1.1.3 Geodesics and Arc Length; 1.1.4 Measure and Integration on Pn; 1.1.5 Differential Operators on Pn; 1.1.6 A List of the Main Formulas Derived in Section 1.1; 1.1.7 An Application to Multivariate Statistics; 1.2 Special Functions on Pn; 1.2.1 Power and Gamma Functions; 1.2.2 K-Bessel Functions; 1.2.3 Spherical Functions; 1.2.4 The Wishart Distribution 1.2.5 Richards' Extension of the Asymptotics of Spherical Functions for P3 to Pn for General n1.3 Harmonic Analysis on Pn in Polar Coordinates; 1.3.1 Properties of the Helgason-Fourier Transform on Pn; 1.3.2 Beginning of the Discussion of Part (1) of Theorem 1.3.1-Steps 1 and 2; 1.3.3 End of the Discussion of Part (1) of Theorem 1.3.1-Steps 3 and 4; 1.3.4 Applications-Richards' Central Limit Theorem for K-Invariant Functions on Pn; 1.3.5 Quantum Chaos and Random Matrix Theory; 1.3.6 Other Directions in the Labyrinth; 1.4 Fundamental Domains for Pn/GL(n, Z); 1.4.1 Introduction 1.4.2 Minkowski's Fundamental Domain1.4.3 Grenier's Fundamental Domain; Grenier's Reduction Algorithm; 1.4.4 Integration over Fundamental Domains; 1.5 Maass Forms for GL(n, Z) and Harmonic Analysis on Pn/GL(n, Z); 1.5.1 Analytic Continuation of Eisenstein Series by the Method of Inserting Larger Parabolic Subgroups; 1.5.2 Hecke Operators and Analytic Continuation of L-Functions Associated with Maass Forms by the Method of Theta Functions; 1.5.3 Fourier Expansions of Eisenstein Series; Generalities on Fourier Expansions of Eisenstein Series; Remarks on Maass Cusp Forms 1.5.4 Update on Maass Cusp Forms for SL(3, Z) and L-Functions Plus Truncating Eisenstein SeriesMaass Cusp Forms for SL(3, Z) and L-Functions; Langlands' Inner Product Formulas for Truncated Eisenstein Series; 1.5.5 Remarks on Harmonic Analysis on the Fundamental Domain; 1.5.6 Finite and Other Analogues; 2 The General Noncompact Symmetric Space; 2.1 Geometry and Analysis on G/K; 2.1.1 Symmetric Spaces, Lie Groups, and Lie Algebras; 2.1.2 Examples of Symmetric Spaces; Plan for Construction of Noncompact Symmetric Spaces of Type III; Type a Examples; Type c Examples 2.1.3 Cartan, Iwasawa, and Polar Decompositions, RootsThree Examples of Iwasawa Decompositions of Real Semisimple Lie Algebras; Examples of the Polar Decomposition; 2.1.4 Geodesics and the Weyl Group; 2.1.5 Integral Formulas; Examples; Invariant Volume Elements on the Symmetric Spaces of GL(n, R) and Sp(n, R); 2.1.6 Invariant Differential Operators; 2.1.7 Special Functions and Harmonic Analysis on Symmetric Spaces; 2.1.8 An Example of a Symmetric Space of Type IV: The Quaternionic Upper Half 3-Space; 2.2 Geometry and Analysis on ""026E30F G/K; 2.2.1 Fundamental Domains; 2.2.2 Automorphic Forms
• Edition: Second edition
• Publisher Details: New York, NY : Springer
• Publication Date: 2016
• Extent: 1 online resource (xv, 487 pages), illustrations (some color)
• Subjects: 515/.2433; Mathematics; Harmonic analysis; Symmetric spaces; Harmonic analysis; Symmetric spaces; Mathematics -- Number Theory; Mathematics -- Geometry -- General; Mathematics -- Combinatorics; Mathematics -- Applied; Mathematics -- Probability & Statistics -- General; Number theory; Geometry; Combinatorics & graph theory; Applied mathematics; Probability & statistics; Number theory; Geometry; Combinatorics; Mathematical statistics; Mathematics -- Mathematical Analysis; Complex analysis, complex variables; Electronic books
• Languages: English
• ISBNs: 9781493934089; 1493934082; 1493934066; 9781493934065
• Related ISBNs: 9781493934065
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed May 4, 2016).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.