Download or read book Regularity Theory of Fourier Integral Operators with Complex Phases and Singularities of Affine Fibrations written by Michael Ruzhansky and published by . This book was released on 2001 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book New Developments in Pseudo Differential Operators written by Luigi Rodino and published by Springer Science & Business Media. This book was released on 2009-01-06 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of peer-reviewed papers related to lectures on pseudo-differential operators presented at the meeting of the ISAAC Group in Pseudo-Differential Operators (IGPDO) held on August 13-18, 2007, and invited papers by experts in the field.

Download or read book Pseudo Differential Operators and Symmetries written by Michael V. Ruzhansky and published by Springer Science & Business Media. This book was released on 2009-10-19 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the development of the theory of pseudo-di?erential n operators on spaces with symmetries. Such spaces are the Euclidean space R ,the n torus T , compact Lie groups and compact homogeneous spaces. The book consists of several parts. One of our aims has been not only to present new results on pseudo-di?erential operators but also to show parallels between di?erent approaches to pseudo-di?erential operators on di?erent spaces. Moreover, we tried to present the material in a self-contained way to make it accessible for readers approaching the material for the ?rst time. However, di?erent spaces on which we develop the theory of pseudo-di?er- tial operators require di?erent backgrounds. Thus, while operators on the - clidean space in Chapter 2 rely on the well-known Euclidean Fourier analysis, pseudo-di?erentialoperatorsonthetorusandmoregeneralLiegroupsinChapters 4 and 10 require certain backgrounds in discrete analysis and in the representation theory of compact Lie groups, which we therefore present in Chapter 3 and in Part III,respectively. Moreover,anyonewhowishestoworkwithpseudo-di?erential- erators on Lie groups will certainly bene?t from a good grasp of certain aspects of representation theory. That is why we present the main elements of this theory in Part III, thus eliminating the necessity for the reader to consult other sources for most of the time. Similarly, the backgrounds for the theory of pseudo-di?erential 3 operators on S and SU(2) developed in Chapter 12 can be found in Chapter 11 presented in a self-contained way suitable for immediate use.

Download or read book Hyperbolic Problems Theory Numerics Applications written by Heinrich Freistühler and published by Springer Science & Business Media. This book was released on 2002-01-01 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics. The mathematical theory of hyperbolic equations has recently made considerable progress. Accurate and efficient numerical schemes for computation have been and are being further developed. This two-volume set of conference proceedings contains about 100 refereed and carefully selected papers. The books are intended for researchers and graduate students in mathematics, science and engineering interested in the most recent results in theory and practice of hyperbolic problems. Applications touched in these proceedings concern one-phase and multiphase fluid flow, phase transitions, shallow water dynamics, elasticity, extended thermodynamics, electromagnetism, classical and relativistic magnetohydrodynamics, cosmology. Contributions to the abstract theory of hyperbolic systems deal with viscous and relaxation approximations, front tracking and wellposedness, stability of shock profiles and multi-shock patterns, traveling fronts for transport equations. Numerically oriented articles study finite difference, finite volume, and finite element schemes, adaptive, multiresolution, and artificial dissipation methods.

Download or read book Wave Packet Analysis of Feynman Path Integrals written by Fabio Nicola and published by Springer Nature. This book was released on 2022-07-28 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this monograph is to offer an accessible and essentially self-contained presentation of some mathematical aspects of the Feynman path integral in non-relativistic quantum mechanics. In spite of the primary role in the advancement of modern theoretical physics and the wide range of applications, path integrals are still a source of challenging problem for mathematicians. From this viewpoint, path integrals can be roughly described in terms of approximation formulas for an operator (usually the propagator of a Schrödinger-type evolution equation) involving a suitably designed sequence of operators. In keeping with the spirit of harmonic analysis, the guiding theme of the book is to illustrate how the powerful techniques of time-frequency analysis - based on the decomposition of functions and operators in terms of the so-called Gabor wave packets – can be successfully applied to mathematical path integrals, leading to remarkable results and paving the way to a fruitful interaction. This monograph intends to build a bridge between the communities of people working in time-frequency analysis and mathematical/theoretical physics, and to provide an exposition of the present novel approach along with its basic toolkit. Having in mind a researcher or a Ph.D. student as reader, we collected in Part I the necessary background, in the most suitable form for our purposes, following a smooth pedagogical pattern. Then Part II covers the analysis of path integrals, reflecting the topics addressed in the research activity of the authors in the last years.

Download or read book Singular fibrations with affine fibers with applications to the regularity theory of Fourier Integral Operators written by Mikhail Vladimirovich Ruzhansky and published by . This book was released on 1998 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Methods for Partial Differential Equations written by Marcelo R. Ebert and published by Birkhäuser. This book was released on 2018-02-23 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of different topics related to the theory of partial differential equations. Selected exercises are included at the end of each chapter to prepare readers for the “research project for beginners” proposed at the end of the book. It is a valuable resource for advanced graduates and undergraduate students who are interested in specializing in this area. The book is organized in five parts: In Part 1 the authors review the basics and the mathematical prerequisites, presenting two of the most fundamental results in the theory of partial differential equations: the Cauchy-Kovalevskaja theorem and Holmgren's uniqueness theorem in its classical and abstract form. It also introduces the method of characteristics in detail and applies this method to the study of Burger's equation. Part 2 focuses on qualitative properties of solutions to basic partial differential equations, explaining the usual properties of solutions to elliptic, parabolic and hyperbolic equations for the archetypes Laplace equation, heat equation and wave equation as well as the different features of each theory. It also discusses the notion of energy of solutions, a highly effective tool for the treatment of non-stationary or evolution models and shows how to define energies for different models. Part 3 demonstrates how phase space analysis and interpolation techniques are used to prove decay estimates for solutions on and away from the conjugate line. It also examines how terms of lower order (mass or dissipation) or additional regularity of the data may influence expected results. Part 4 addresses semilinear models with power type non-linearity of source and absorbing type in order to determine critical exponents: two well-known critical exponents, the Fujita exponent and the Strauss exponent come into play. Depending on concrete models these critical exponents divide the range of admissible powers in classes which make it possible to prove quite different qualitative properties of solutions, for example, the stability of the zero solution or blow-up behavior of local (in time) solutions. The last part features selected research projects and general background material.

Download or read book Evolution Equations written by Rainer H. Picard and published by . This book was released on 2003 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Topics in the Regularity Theory of Fourier Integral Operators written by Norberto Laghi and published by . This book was released on 2004 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Multivariable Orthogonal Polynomials and Quantum Grassmanniams i e Grassmannians written by Jasper V. Stokman and published by . This book was released on 2001 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Russian Mathematical Surveys written by and published by . This book was released on 2000 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Hyperbolic Problems Theory Numerics Applications written by Michael Fey and published by Birkhäuser. This book was released on 2012-12-06 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: [Infotext]((Kurztext))These are the proceedings of the 7th International Conference on Hyperbolic Problems, held in Zürich in February 1998. The speakers and contributors have been rigorously selected and present the state of the art in this field. The articles, both theoretical and numerical, encompass a wide range of applications, such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phenomena and geometrical optics. ((Volltext))These proceedings contain, in two volumes, approximately one hundred papers presented at the conference on hyperbolic problems, which has focused to a large extent on the laws of nonlinear hyperbolic conservation. Two-fifths of the papers are devoted to mathematical aspects such as global existence, uniqueness, asymptotic behavior such as large time stability, stability and instabilities of waves and structures, various limits of the solution, the Riemann problem and so on. Roughly the same number of articles are devoted to numerical analysis, for example stability and convergence of numerical schemes, as well as schemes with special desired properties such as shock capturing, interface fitting and high-order approximations to multidimensional systems. The results in these contributions, both theoretical and numerical, encompass a wide range of applications such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phenomena and geometrical optics.

Download or read book Global and Local Regularity of Fourier Integral Operators on Weighted and Unweighted Spaces written by David Dos Santos Ferreira and published by . This book was released on 2014-10-03 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Reviews written by and published by . This book was released on 2002 with total page 964 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Integral Fourier Operators written by Michèle Audin and published by Universitätsverlag Potsdam. This book was released on 2018-04-17 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of contributions based on lectures delivered at a school on Fourier Integral Operators held in Ouagadougou, Burkina Faso, 14–26 September 2015, provides an introduction to Fourier Integral Operators (FIO) for a readership of Master and PhD students as well as any interested layperson. Considering the wide spectrum of their applications and the richness of the mathematical tools they involve, FIOs lie the cross-road of many a field. This volume offers the necessary background, whether analytic or geometric, to get acquainted with FIOs, complemented by more advanced material presenting various aspects of active research in that area.

Download or read book Semi classical Analysis written by Victor Guillemin and published by . This book was released on 2013 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Holomorphic Curves in Low Dimensions written by Chris Wendl and published by Springer. This book was released on 2018-06-28 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three. The first half of the book focuses on McDuff's characterization of symplectic rational and ruled surfaces, one of the classic early applications of holomorphic curve theory. The proof presented here uses the language of Lefschetz fibrations and pencils, thus it includes some background on these topics, in addition to a survey of the required analytical results on holomorphic curves. Emphasizing applications rather than technical results, the analytical survey mostly refers to other sources for proofs, while aiming to provide precise statements that are widely applicable, plus some informal discussion of the analytical ideas behind them. The second half of the book then extends this program in two complementary directions: (1) a gentle introduction to Gromov-Witten theory and complete proof of the classification of uniruled symplectic 4-manifolds; and (2) a survey of punctured holomorphic curves and their applications to questions from 3-dimensional contact topology, such as classifying the symplectic fillings of planar contact manifolds. This book will be particularly useful to graduate students and researchers who have basic literacy in symplectic geometry and algebraic topology, and would like to learn how to apply standard techniques from holomorphic curve theory without dwelling more than necessary on the analytical details. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019