Linear Partial Differential Operators in Gevrey Spaces

Author: Luigi Rodino

Publisher: World Scientific

ISBN: 9789810208455

Category: Mathematics

Page: 251

View: 7409

The book is devoted to new and classical results of the theory of linear partial differential operators in Gevrey spaces. The ?microlocal approach? is adopted, by using pseudo-differential operators, wave front sets and Fourier integral operators.Basic results for Schwartz-distributions, cì and analytic classes are also included, concerning hypoellipticity, solvability and propagation of singularities.Also included is a self-contained exposition of the calculus of the pseudo-differential operators of infinite order.

Advances in Pseudo-Differential Operators

Author: Ryuichi Ashino,Paolo Boggiatto,Man-Wah Wong

Publisher: Birkhäuser

ISBN: 3034878400

Category: Mathematics

Page: 236

View: 3438

This volume consists of the plenary lectures and invited talks in the special session on pseudo-differential operators given at the Fourth Congress of the International Society for Analysis, Applications and Computation (ISAAC) held at York University in Toronto, August 11-16, 2003. The theme is to look at pseudo-differential operators in a very general sense and to report recent advances in a broad spectrum of topics, such as pde, quantization, filters and localization operators, modulation spaces, and numerical experiments in wavelet transforms and orthonormal wavelet bases.

Partial Differential Equations

Approximate Solutions in Scales of Functional Spaces

Author: Todor V. Gramchev,Petar R. Popivanov

Publisher: Wiley-VCH


Category: Science

Page: 156

View: 5640

The applications of methods from microlocal analysis for PDE have been a fast developing area during the last years. The authors, both are well known in the community, publish for the first time some of their research results in a summarized form. The essential point of the approach is the use of the various types of approximate (asymptotic) solutions in the study of differential equations in the smooth and the Gevrey spaces. In this volume, the authors deal with the following themes: Microlocal properties of pseudodifferential operators with multiple characteristics of involutive type in the framework of the Sobolev spaces; Abstract schemes for constructing approximate solutions to linear partial differential equations with characteristics of constant multiplicity m greater than or equal 2 in the framework of Gevrey spaces; Local solvability, hypoellipticity and singular solutions in Gevrey spaces; Global Gevrey solvability on the torus for linear partial differential equations; Applications of asymptotic methods for local (non)solvability for quasihomogeneous operators; Applications of Airy asymptotic solutions to degenerate oblique derivative problems for second order strictly hyperbolic equations; Approximate Gevrey normal forms of analytic involutions and analytic glancing hypersurfaces with applications for effective stability estimates for billiard ball maps.

Pseudo-Differential Operators and Related Topics

Author: Paolo Boggiatto,Luigi Rodino,Joachim Toft,M. W. Wong

Publisher: Springer Science & Business Media

ISBN: 3764375140

Category: Mathematics

Page: 244

View: 8893

Contains articles based on lectures given at the International Conference on Pseudo-differential Operators and Related Topics at Vaxjo University in Sweden from June 22 to June 25, 2005. Sixteen refereed articles cover a spectrum of topics such as partial differential equations, Wigner transforms, mathematical physics, and more.

Hyperbolic Problems and Regularity Questions

Author: Mariarosaria Padula,Luisa Zanghirati

Publisher: Springer Science & Business Media

ISBN: 3764374519

Category: Mathematics

Page: 231

View: 8738

This book discusses new challenges in the quickly developing field of hyperbolic problems. Particular emphasis lies on the interaction between nonlinear partial differential equations, functional analysis and applied analysis as well as mechanics. The book originates from a recent conference focusing on hyperbolic problems and regularity questions. It is intended for researchers in functional analysis, PDE, fluid dynamics and differential geometry.

Degenerate Differential Equations in Banach Spaces

Author: Angelo Favini,Atsushi Yagi

Publisher: CRC Press

ISBN: 9780824716776

Category: Mathematics

Page: 336

View: 7654

This work presents a detailed study of linear abstract degenerate differential equations, using both the semigroups generated by multivalued (linear) operators and extensions of the operational method from Da Prato and Grisvard. The authors describe the recent and original results on PDEs and algebraic-differential equations, and establishes the analyzability of the semigroup generated by some degenerate parabolic operators in spaces of continuous functions.

New Developments in Pseudo-Differential Operators

ISAAC Group in Pseudo-Differential Operators (IGPDO), Middle East Technical University, Ankara,Turkey, August 2007

Author: Luigi Rodino,M. W. Wong

Publisher: Springer Science & Business Media

ISBN: 3764389699

Category: Mathematics

Page: 332

View: 7951

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.

Partial Differential Equations and Mathematical Physics

In Memory of Jean Leray

Author: Kunihiko Kajitani,Jean Vaillant

Publisher: Springer Science & Business Media

ISBN: 1461200113

Category: Mathematics

Page: 243

View: 6183

The 17 invited research articles in this volume, all written by leading experts in their respective fields, are dedicated to the great French mathematician Jean Leray. A wide range of topics with significant new results---detailed proofs---are presented in the areas of partial differential equations, complex analysis, and mathematical physics. Key subjects are: * Treated from the mathematical physics viewpoint: nonlinear stability of an expanding universe, the compressible Euler equation, spin groups and the Leray--Maslov index, * Linked to the Cauchy problem: an intermediate case between effective hyperbolicity and the Levi condition, global Cauchy--Kowalewski theorem in some Gevrey classes, the analytic continuation of the solution, necessary conditions for hyperbolic systems, well posedness in the Gevrey class, uniformly diagonalizable systems and reduced dimension, and monodromy of ramified Cauchy problem. Additional articles examine results on: * Local solvability for a system of partial differential operators, * The hypoellipticity of second order operators, * Differential forms and Hodge theory on analytic spaces, * Subelliptic operators and sub- Riemannian geometry. Contributors: V. Ancona, R. Beals, A. Bove, R. Camales, Y. Choquet- Bruhat, F. Colombini, M. De Gosson, S. De Gosson, M. Di Flaviano, B. Gaveau, D. Gourdin, P. Greiner, Y. Hamada, K. Kajitani, M. Mechab, K. Mizohata, V. Moncrief, N. Nakazawa, T. Nishitani, Y. Ohya, T. Okaji, S. Ouchi, S. Spagnolo, J. Vaillant, C. Wagschal, S. Wakabayashi The book is suitable as a reference text for graduate students and active researchers.

Pseudo-Differential Operators: Analysis, Applications and Computations

Author: Luigi Rodino,M. W. Wong,Hongmei Zhu

Publisher: Springer Science & Business Media

ISBN: 9783034800495

Category: Mathematics

Page: 308

View: 9638

This volume consists of eighteen peer-reviewed papers related to lectures on pseudo-differential operators presented at the meeting of the ISAAC Group in Pseudo-Differential Operators (IGPDO) held at Imperial College London on July 13-18, 2009. Featured in this volume are the analysis, applications and computations of pseudo-differential operators in mathematics, physics and signal analysis. This volume is a useful complement to the volumes “Advances in Pseudo-Differential Operators”, “Pseudo-Differential Operators and Related Topics”, “Modern Trends in Pseudo-Differential Operators”, “New Developments in Pseudo-Differential Operators” and “Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations” published in the same series in, respectively, 2004, 2006, 2007, 2009 and 2010.

Microlocal Analysis and Spectral Theory

Author: Luigi Rodino

Publisher: Springer Science & Business Media

ISBN: 9780792345442

Category: Mathematics

Page: 444

View: 4551

There has been considerable recent progress in the field of microlocal analysis. In a broad sense the subject is the modern version of the classical Fourier technique for solving partial differential equations, with the localization process taking account of dual variables. The tools of pseudo-differential operators, wave-front sets and Fourier integral operators have now conferred a mature form on the theory of linear partial differential operators in the frame of Schwartz distributions or other generalized functions. At the same time, microlocal analysis has assumed an important role as an independent part of analysis, with other applications throughout mathematics and physics, one major theme being spectral theory for the Schrödinger equation in quantum mechanics. The papers collected here emphasize the topics of microlocal methods in the study of linear PDEs (analytic-Gevrey regularity of the solutions, elliptic boundary value problems, higher microlocalization), and applications to spectral theory (Schrödinger equation, asymptotic behavior of the eigenvalues, semi-classical analysis in large dimensions and statistical mechanics). Audience: Accessible to a wide audience, including graduate students in analysis and non-specialists from mathematics and physics.

Fourier Analysis

Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations

Author: Michael Ruzhansky,Ville Turunen

Publisher: Springer Science & Business Media

ISBN: 3319025503

Category: Mathematics

Page: 415

View: 5754

This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudo-differential operators, partial differential equations, and time-frequency analysis. It is based on lectures given at the international conference “Fourier Analysis and Pseudo-Differential Operators,” June 25–30, 2012, at Aalto University, Finland. This collection of 20 refereed articles is based on selected talks and presents the latest advances in the field. The conference was a satellite meeting of the 6th European Congress of Mathematics, which took place in Krakow in July 2012; it was also the 6th meeting in the series “Fourier Analysis and Partial Differential Equations.”