A.T.Fomenko and A.S.Mishchenko / Moscow State University, Russia

A Short Course in Differential Geometry and Topology

Hb 350pp 2009
9781904868323


This volume is intended for graduate and research students in mathematics and physics. It covers general topology, nonlinear co-ordinate systems, theory of smooth manifolds, theory of curves and surfaces, transformation groups, tensor analysis and Riemannian geometry, theory of integration and homologies, fundamental groups and variational principles in Riemannian geometry. The text is presented in a form that is easily accessible to students and is supplemented by a large number of examples, problems, drawings and appendices.

A.A.Kilbas and A.A.Prudnikov, Belarusian State University, Minsk

Handbook of Mellin Transforms

800pp Hbk 2009
9781904868408


This volume presents the tables of formulae for the evaluation of Mellin Transforms of elementary and special functions. The Handbook includes some formulae obtained by the authors and published for the first time. The tables are prefaced by a summary of notation for special functions and certain constants. The appendix contains some properties of the Mellin transform and applications. The results in tables are important for applications in different areas of mathematics, physics, mechanics, engineering, chemistry, biology and other applied sciences. The Handbook is a useful source of reference for graduate students and researchers.

Arnold,I.V. et al. (ed)

Vladimir I. Arnold - Collected Works
Representations of Functions, Celestial Mechanics, and KAM Theory 1957-1965

Series: Vladimir I. Arnold - Collected Works , Vol. 1

2009, Approx. 480 p., Hardcover

ISBN: 978-3-642-01741-4

Due: June 2009

About this book

Vladimir Arnold is one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work.

At the same time he is one of the most prolific and outstanding mathematical authors. This first volume of his Collected Works focuses on representations of functions, celestial mechanics, and KAM theory.

Written for:

Researchers and graduate students in mathematics and physics

Edited by: Gestur Olafsson, Louisiana State University, Baton Rouge, LA,
and Henrik Schlichtkrull, University of Copenhagen, Denmark

The Selected Works of Sigurdur Helgason

Collected Works, Volume: 22
2009; 715 pp; hardcover
ISBN-13: 978-0-8218-4753-4
Expected publication date is July 29, 2009.

Sigurdur Helgason is a leading expert in harmonic analysis and integral geometry on symmetric spaces. His work has had, and continues to have, a profound influence on the field. Helgason's work is marked by an interplay of analysis, geometry, and representation theory. The articles collected here cover invariant differential operators, geometric properties of solutions to differential equations on symmetric spaces, double fibrations in integral geometry, spherical functions and spherical transforms, duality for symmetric spaces, representation theory, and the Fourier transform on $G/K$. The papers are supplemented by an introductory essay by Helgason.

This Selecta of Sigurdur Helgason's important papers will be a valuable resource to research mathematicians and graduate students.

Readership

Graduate students and research mathematicians interested in harmonic analyis on symmetric spaces, Radon transforms, and representations of semi-simple Lie groups.

Table of Contents

• Multipliers of Banach algebras
• Differential operators on homogeneous spaces
• Fundamental solutions of invariant differential operators on symmetric spaces
• Duality and Radon transform for symmetric spaces
• Fundamental solutions of invariant differential operators on symmetric spaces
• The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassman manifolds
• Radon-Fourier transforms on symmetric spaces and related group representations
• A duality in integral geometry on symmetric spaces
• Totally geodesic spheres in compact symmetric spaces
• An analogue of the Paley-Wiener theorem for the Fourier transform on certain symmetric spaces
• (with A. Koranyi), A Fatou-type theorem for harmonic functions on symmetric spaces
• (with K. Johnson), The bounded spherical functions on symmetric spaces
• Applications of the Radon transform to representations of semisimple Lie groups
• A duality for symmetric spaces with applications to group representations
• Group representations and symmetric spaces
• A formula for the radial part of the Laplace-Beltrami operator
• Paley-Wiener theorems and surjectivity of invariant differential operators on symmetric spaces and Lie groups
• The surjectivity of invariant differential operators on symmetric spaces I
• Eigenspaces of the Laplacian; integral representations and irreducibility
• A duality for symmetric spaces with applications to group representations, II. Differential equations and Eigenspace representations
• A duality for symmetric spaces with applications to group representations III. Tangent space analysis
• (with F. Gonzalez), Invariant differential operators on Grassmann manifolds
• Value-distribution theory for holomorphic almost periodic functions
• The totally-geodesic Radon transform on constant curvature spaces
• Some results on invariant differential operators on symmetric spaces
• The flat horocycle transform for a symmetric space
• Huygens' principle for wave equations on symmetric spaces
• Radon transforms for double fibrations. Examples and viewpoints.
• Integral geometry and multitemporal wave equations
• (with H. Schlichtkrull), The Paley-Wiener space for the multitemporal wave equation
• The Abel, Fourier, and Radon transforms on symmetric spaces
• The inversion of the x-ray transform on a compact symmetric space