An Introduction
Author: Alain Grigis,Johannes Sjöstrand
Publisher: Cambridge University Press
ISBN: 9780521449861
Category: Mathematics
Page: 151
View: 5334
This book corresponds to a graduate course given many times by the authors, and should prove to be useful to mathematicians and theoretical physicists.
Partial Differential Equations IV
Microlocal Analysis and Hyperbolic Equations
Author: Yu.V. Egorov,M.A. Shubin
Publisher: Springer Science & Business Media
ISBN: 3662092077
Category: Mathematics
Page: 244
View: 7860
A two-part monograph covering recent research in an important field, previously scattered in numerous journals, including the latest results in the theory of mixed problems for hyperbolic operators. The book is hence of immense value to graduate students and researchers in partial differential equations and theoretical physics.
Author: Yu.V. Egorov,M.A. Shubin
Publisher: Springer Science & Business Media
ISBN: 3662092077
Category: Mathematics
Page: 244
View: 7860
An Introduction to Semiclassical and Microlocal Analysis
Author: Andre Martinez
Publisher: Springer Science & Business Media
ISBN: 9780387953441
Category: Mathematics
Page: 190
View: 7138
General Theory of Partial Differential Equations and Microlocal Analysis
Author: Min-You Qi,L Rodino
Publisher: CRC Press
ISBN: 9780582292123
Category: Mathematics
Page: 240
View: 3562
Lectures on Nonlinear Hyperbolic Differential Equations
Author: Lars Hörmander
Publisher: Springer Science & Business Media
ISBN: 9783540629214
Category: Mathematics
Page: 289
View: 4035
Seminar on Micro-Local Analysis. (AM-93)
Author: Victor Guillemin,Masaki Kashiwara,Takahiro Kawai
Publisher: Princeton University Press
ISBN: 1400881579
Category: Mathematics
Page: 152
View: 4775
Microlocal Analysis and Spectral Theory
Author: Luigi Rodino
Publisher: Springer Science & Business Media
ISBN: 9401156263
Category: Mathematics
Page: 444
View: 2041
Semiclassical Analysis
Author: Maciej Zworski
Publisher: American Mathematical Soc.
ISBN: 0821883208
Category: Mathematics
Page: 431
View: 4911
Spectral Asymptotics in the Semi-Classical Limit
Author: M. Dimassi,J. Sjostrand
Publisher: Cambridge University Press
ISBN: 9780521665445
Category: Mathematics
Page: 227
View: 2484
Microlocal Analysis and Precise Spectral Asymptotics
Author: Victor Ivrii
Publisher: Springer Science & Business Media
ISBN: 3662124963
Category: Mathematics
Page: 733
View: 990
Pseudo-differential Operators and the Nash-Moser Theorem
Author: Serge Alinhac,Patrick Gérard
Publisher: American Mathematical Soc.
ISBN: 0821834541
Category: Mathematics
Page: 168
View: 4414
Pseudodifferential Operators and Spectral Theory
Author: M.A. Shubin
Publisher: Springer Science & Business Media
ISBN: 3642565794
Category: Mathematics
Page: 288
View: 4071
Spectral Theory, Microlocal Analysis, Singular Manifolds
Advances in Partial Differential Equations
Author: Michael Demuth,Elmar Schrohe,Bert-Wolfgang Schulze,Johannes Sjöstrand
Publisher: Wiley-VCH
ISBN: 9783527401208
Category: Mathematics
Page: 368
View: 1386
The spectral theory of differential operators is a challenging subject with deep connections to many branches of mathematics and mathematical physics. It is a central issue in this volume of Advances in Partial Differential Equations The first contribution addresses domain perturbations for generalized Schr?dinger operators and the influence of the capacity on spectral data. There follows an article discussing the minimal smoothness assumptions on the domain under which the asymptotics of the counting function for the eigenvalues of elliptic boundary value problems can be determined. Systems of h-pseudo-differential operators on the half-line are studied in the next paper. The results concern existence and distribution of resonances for various semi-classical regimes. Three further articles are devoted to the regularity and symptotics of solutions to partial differential equations on singular manifolds. A very efficient tool is the combination of suitable operator algebras and pseudo-differential calculi with sufficiently rich symbolic structures. One paper considers the case of manifolds with non-compact ends, another the case of higher cuspidal singularities. A final contribution treats degenerate hyperbolic equations.
Author: Michael Demuth,Elmar Schrohe,Bert-Wolfgang Schulze,Johannes Sjöstrand
Publisher: Wiley-VCH
ISBN: 9783527401208
Category: Mathematics
Page: 368
View: 1386
Algebraic Analysis of Differential Equations
from Microlocal Analysis to Exponential Asymptotics
Author: T. Aoki,H. Majima,Y. Takei,N. Tose
Publisher: Springer Science & Business Media
ISBN: 9784431732402
Category: Mathematics
Page: 352
View: 765
This volume contains 23 articles on algebraic analysis of differential equations and related topics, most of which were presented as papers at the conference "Algebraic Analysis of Differential Equations – from Microlocal Analysis to Exponential Asymptotics" at Kyoto University in 2005. This volume is dedicated to Professor Takahiro Kawai, who is one of the creators of microlocal analysis and who introduced the technique of microlocal analysis into exponential asymptotics.
Author: T. Aoki,H. Majima,Y. Takei,N. Tose
Publisher: Springer Science & Business Media
ISBN: 9784431732402
Category: Mathematics
Page: 352
View: 765
Tools for PDE
Pseudodifferential Operators, Paradifferential Operators, and Layer Potentials
Author: Michael Eugene Taylor
Publisher: American Mathematical Soc.
ISBN: 0821843788
Category: MATHEMATICS
Page: 257
View: 9587
This book develops three related tools that are useful in the analysis of partial differential equations (PDEs), arising from the classical study of singular integral operators: pseudodifferential operators, paradifferential operators, and layer potentials. A theme running throughout the work is the treatment of PDE in the presence of relatively little regularity. The first chapter studies classes of pseudodifferential operators whose symbols have a limited degree of regularity; the second chapter shows how paradifferential operators yield sharp estimates on the action of various nonlinear operators on function spaces. The third chapter applies this material to an assortment of results in PDE, including regularity results for elliptic PDE with rough coefficients, planar fluid flows on rough domains, estimates on Riemannian manifolds given weak bounds on Ricci tensor, div-curl estimates, and results on propagation of singularities for wave equations with rough coefficients. The last chapter studies the method of layer potentials on Lipschitz domains, concentrating on applications to boundary problems for elliptic PDE with variable coefficients.
Author: Michael Eugene Taylor
Publisher: American Mathematical Soc.
ISBN: 0821843788
Category: MATHEMATICS
Page: 257
View: 9587
Elementary Introduction to the Theory of Pseudodifferential Operators
Author: Xavier Saint Raymond
Publisher: Routledge
ISBN: 1351452924
Category: Mathematics
Page: 120
View: 3906
Lectures on Linear Partial Differential Equations
Author: Grigoriĭ Ilʹich Eskin
Publisher: American Mathematical Soc.
ISBN: 0821852841
Category: Mathematics
Page: 410
View: 6026
Evolution Equations
Author: David Ellwood,Igor Rodnianski,Gigliola Staffilani,Jared Wunsch
Publisher: American Mathematical Soc.
ISBN: 0821868616
Category: Mathematics
Page: 572
View: 7452
Phase Space Analysis of Partial Differential Equations
Author: Antonio Bove,Ferruccio Colombini,Daniele Del Santo
Publisher: Springer Science & Business Media
ISBN: 9780817645212
Category: Mathematics
Page: 343
View: 2001
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: 1158