This particular textual content is an creation to harmonic research at the least difficult symmetric areas, specifically Euclidean area, the field, and the Poincaré top part plane. This booklet is meant for starting graduate scholars in arithmetic or researchers in physics or engineering. Written with an off-the-cuff type, the booklet areas an emphasis on motivation, concrete examples, heritage, and, especially, purposes in arithmetic, information, physics, and engineering.
Many corrections and updates were integrated during this re-creation. Updates contain discussions of P. Sarnak and others' paintings on quantum chaos, the paintings of T. Sunada, Marie-France Vignéras, Carolyn Gordon, and others on Mark Kac's query "Can you pay attention the form of a drum?", A. Lubotzky, R. Phillips and P. Sarnak's examples of Ramanujan graphs, and, ultimately, the author's comparisons of continuing thought with the finite analogues.
Topics featured during the textual content contain inversion formulation for Fourier transforms, relevant restrict theorems, Poisson's summation formulation and purposes in crystallography and quantity idea, purposes of round harmonic research to the hydrogen atom, the Radon rework, non-Euclidean geometry at the Poincaré top part aircraft H or unit disc and functions to microwave engineering, basic domain names in H for discrete teams Γ, tessellations of H from such discrete staff activities, automorphic kinds, and the Selberg hint formulation and its purposes in spectral conception in addition to quantity theory.
Read Online or Download Harmonic Analysis on Symmetric Spaces_Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane PDF
Best Abstract books
This 1968 version covers the next subject matters: Orientation; units and areas; sequences and sequence; degree and integration; degree thought; continuity; derivatives; and stieltjes integrals.
During this well-written presentation, inspired by means of a number of examples and difficulties, the authors introduce the fundamental conception of braid teams, highlighting numerous definitions that exhibit their equivalence; this is often through a therapy of the connection among braids, knots and hyperlinks. vital effects then deal with the linearity and orderability of the topic.
This quantity of the Encyclopaedia offers a latest method of homological algebra, that is in response to the systematic use of the terminology and concepts of derived different types and derived functors. The e-book includes purposes of homological algebra to the idea of sheaves on topological areas, to Hodge idea, and to the idea of sheaves on topological areas, to Hodge conception, and to the idea of modules over earrings of algebraic differential operators (algebraic D-modules).
This publication offers an obtainable advent to category box thought. It takes a standard strategy, yet in a way that is cleanser and extra streamlined than such a lot different books in this subject. The publication has been class-tested, and the writer has incorporated workouts.
Additional info for Harmonic Analysis on Symmetric Spaces_Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane