Dirichlet Series

Principles and Methods

Author: S. Mandelbrojt

Publisher: Springer Science & Business Media

ISBN: 9401031347

Category: Mathematics

Page: 176

View: 5253

It is not our intention to present a treatise on Dirichlet series. This part of harmonic analysis is so vast, so rich in publications and in 'theorems' that it appears to us inconceivable and, to our mind, void of interest to assemble anything but a restricted (but relatively complete) branch of the theory. We have not tried to give an account of the very important results of G. P6lya which link his notion of maximum density to the analytic continuation of the series, nor the researches to which the names of A. Ostrowski and V. Bernstein are intimately attached. The excellent book of the latter, which was published in the Collection Borel more than thirty years ago, gives an account of them with all the clarity one can wish for. Nevertheless, some scattered results proved by these authors have found their place among the relevant results, partly by their statements, partly as a working tool. We have adopted a more personal point of view, in explaining the methods and the principles (as the title of the book indicates) that originate in our research work and provide a collection of results which we develop here; we have also included others, due to present-day authors, which enable us to form a coherent whole.

Encyclopaedia of Mathematics

Coproduct — Hausdorff — Young Inequalities

Author: M. Hazewinkel

Publisher: Springer

ISBN: 1489937951

Category: Mathematics

Page: 963

View: 2895

Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory

Proceedings of the Bretton Woods Workshop on Multiple Dirichlet Series, Bretton Woods, New Hampshire, July 11-14, 2005

Author: Bretton Woods Workshop on Multiple Dirichlet Series

Publisher: American Mathematical Soc.

ISBN: 0821839632

Category: Mathematics

Page: 303

View: 1840

Multiple Dirichlet series are Dirichlet series in several complex variables. A multiple Dirichlet series is said to be perfect if it satisfies a finite group of functional equations and has meromorphic continuation everywhere. The earliest examples came from Mellin transforms of metaplectic Eisenstein series and have been intensively studied over the last twenty years. More recently, many other examples have been discovered and it appears that all the classical theorems on moments of $L$-functions as well as the conjectures (such as those predicted by random matrix theory) can now be obtained via the theory of multiple Dirichlet series.Furthermore, new results, not obtainable by other methods, are just coming to light. This volume offers an account of some of the major research to date and the opportunities for the future. It includes an exposition of the main results in the theory of multiple Dirichlet series, and papers on moments of zeta- and $L$-functions, on new examples of multiple Dirichlet series, and on developments in the allied fields of automorphic forms and analytic number theory.

Library of Congress Catalog

Books-Subjects, 1970-1974, Set

Author: United States

Publisher: Rowman & Littlefield Publishers

ISBN: 9780874717853

Category: Subject catalogs

Page: N.A

View: 7872

Biographisch-literarisches Handwörterbuch

für Mathematik, Astronomie, Physik mit Geophysik, Chemie, Kristallographie und verwandte Wissensgebiete ...

Author: Johann Christian Poggendorff,Berend Wilhelm Feddersen,Arthur Oettingen,Hans Stobbe,Paul Franz Wilhelm Weinmeister

Publisher: N.A


Category: Science

Page: N.A

View: 6975

Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems

Author: Dumitru Motreanu,Viorica Venera Motreanu,Nikolaos Papageorgiou

Publisher: Springer Science & Business Media

ISBN: 1461493234

Category: Mathematics

Page: 459

View: 8052

This book focuses on nonlinear boundary value problems and the aspects of nonlinear analysis which are necessary to their study. The authors first give a comprehensive introduction to the many different classical methods from nonlinear analysis, variational principles, and Morse theory. They then provide a rigorous and detailed treatment of the relevant areas of nonlinear analysis with new applications to nonlinear boundary value problems for both ordinary and partial differential equations. Recent results on the existence and multiplicity of critical points for both smooth and nonsmooth functional, developments on the degree theory of monotone type operators, nonlinear maximum and comparison principles for p-Laplacian type operators, and new developments on nonlinear Neumann problems involving non-homogeneous differential operators appear for the first time in book form. The presentation is systematic, and an extensive bibliography and a remarks section at the end of each chapter highlight the text. This work will serve as an invaluable reference for researchers working in nonlinear analysis and partial differential equations as well as a useful tool for all those interested in the topics presented.

Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces

Author: Richard Courant

Publisher: Courier Corporation

ISBN: 0486445526

Category: Mathematics

Page: 330

View: 5982

Originally published: New York: Interscience Publishers, 1950, in series: Pure and applied mathematics (Interscience Publishers); v. 3.

Introduction to Partial Differential Equations and Hilbert Space Methods

Author: Karl E. Gustafson

Publisher: Courier Corporation

ISBN: 0486140873

Category: Mathematics

Page: 480

View: 3357

Easy-to-use text examines principal method of solving partial differential equations, 1st-order systems, computation methods, and much more. Over 600 exercises, with answers for many. Ideal for a 1-semester or full-year course.

The Princeton Companion to Mathematics

Author: Timothy Gowers,June Barrow-Green,Imre Leader

Publisher: Princeton University Press

ISBN: 9781400830398

Category: Mathematics

Page: 1056

View: 6187

This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music--and much, much more. Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics. Accessible in style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties. Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors Presents major ideas and branches of pure mathematics in a clear, accessible style Defines and explains important mathematical concepts, methods, theorems, and open problems Introduces the language of mathematics and the goals of mathematical research Covers number theory, algebra, analysis, geometry, logic, probability, and more Traces the history and development of modern mathematics Profiles more than ninety-five mathematicians who influenced those working today Explores the influence of mathematics on other disciplines Includes bibliographies, cross-references, and a comprehensive index Contributors incude: Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, Béla Bollobás, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevin Buzzard, Peter J. Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford C. Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph W. Dauben, John W. Dawson Jr., Francois de Gandt, Persi Diaconis, Jordan S. Ellenberg, Lawrence C. Evans, Florence Fasanelli, Anita Burdman Feferman, Solomon Feferman, Charles Fefferman, Della Fenster, José Ferreirós, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouvêa, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolò Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, F. E. A. Johnson, Mark Joshi, Kiran S. Kedlaya, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, János Kollár, T. W. Körner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-François Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper Lützen, Des MacHale, Alan L. Mackay, Shahn Majid, Lech Maligranda, David Marker, Jean Mawhin, Barry Mazur, Dusa McDuff, Colin McLarty, Bojan Mohar, Peter M. Neumann, Catherine Nolan, James Norris, Brian Osserman, Richard S. Palais, Marco Panza, Karen Hunger Parshall, Gabriel P. Paternain, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Michael C. Reed, Adrian Rice, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Tilman Sauer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Reinhard Siegmund-Schultze, Gordon Slade, David J. Spiegelhalter, Jacqueline Stedall, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, C. H. Taubes, Rüdiger Thiele, Burt Totaro, Lloyd N. Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, B. Yandell, Eric Zaslow, Doron Zeilberger