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Author: Gerd Grubb
Publisher: Springer Science & Business Media
ISBN: 146120769X
Category : Mathematics
Languages : en
Pages : 536
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Book Description
Pseudodifferential methods are central to the study of partial differential equations, because they permit an "algebraization." The main purpose of this book is to set up an operational calculus for operators defined from differential and pseudodifferential boundary values problems via a resolvent construction. A secondary purposed is to give a complete treatment of the properties of the calculus of pseudodifferential boundary problems with transmission, both the first version by Boutet de Monvel (brought completely up to date in this edition) and in version containing a parameter running in an unbounded set. And finally, the book presents some applications to evolution problems, index theory, fractional powers, spectral theory and singular perturbation theory. Thus the book’s improved proofs and modern points of view will be useful to research mathematicians and to graduate students studying partial differential equations and pseudodifferential operators.
Author: Gerd Grubb
Publisher: Springer Science & Business Media
ISBN: 146120769X
Category : Mathematics
Languages : en
Pages : 536
Get Book Here
Book Description
Pseudodifferential methods are central to the study of partial differential equations, because they permit an "algebraization." The main purpose of this book is to set up an operational calculus for operators defined from differential and pseudodifferential boundary values problems via a resolvent construction. A secondary purposed is to give a complete treatment of the properties of the calculus of pseudodifferential boundary problems with transmission, both the first version by Boutet de Monvel (brought completely up to date in this edition) and in version containing a parameter running in an unbounded set. And finally, the book presents some applications to evolution problems, index theory, fractional powers, spectral theory and singular perturbation theory. Thus the book’s improved proofs and modern points of view will be useful to research mathematicians and to graduate students studying partial differential equations and pseudodifferential operators.
Author: G. Grubb
Publisher: Springer Science & Business Media
ISBN: 1475718985
Category : Science
Languages : en
Pages : 520
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Book Description
CHAPTER 1. STANDARD PSEUDO-DIFFERENTIAL BOUNDARY PROBLEMS AND THEIR REALIZATIONS 1. 1 Introductory remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1. 2 The calculus of pseudo-differential boundary problems . . •. 19 1. 3 Green's formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 1. 4 Realizations and normal boundary conditions . . . . . . . . . . . . . . 39 1. 5 Parameter-ellipticity and parabolicity . . . . . . . . . . . . . . . . . . . 50 1. 6 Adjoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 1. 7 Semiboundedness and coerciveness . . . . . . . . •. . . . . . . . . . . •. . . . 96 CHAPTER 2. THE CALCULUS OF PARAMETER-DEPENDENT OPERATORS 2. 1 Parameter-dependent pseudo-differential operators . . •. . . . . 125 2. 2 The transmission property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 2. 3 Parameter-dependent boundary symbol s . . . . . . . . . . . . . . . . . . . . . 179 2. 4 Operators and kernels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 2. 5 Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 2. 6 Composition of xn-independent boundary symbol operators . . 234 2. 7 Compositions in general . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 2. 8 Strictly homogeneous symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 CHAPTER 3. PARAMETRIX AND RESOLVENT CONSTRUCTIONS 3. 1 Ellipticity. Auxiliary elliptic operators . . . . . . . . . . . . . . . . 280 3. 2 The parametrix construction . . . . . . . . . . •. . . . . . . . . . . . . . . . . . . 297 3. 3 The resolvent of a realization . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 3. 4 Other special cases . . . . . . •. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 CHAPTER 4. SOME APPLICATIONS 4. 1 Evolution problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 4. 2 The heat operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 4. 3 An index formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 4. 4 Complex powers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 4. 5 Spectral asymptotics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 4. 6 Implicit eigenvalue problems . . . . . . . . . . . . . . . . . . . . . . . •. . . . . 437 4. 7 Singular perturbations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449 APPENDIX. VARIOUS PREREQUISITES (A. 1 General notation. A. 2 Functions and distributions. A. 3 Sobolev spaces. A. 4 Spaces over sub sets of mn. A. 5 Spaces over manifolds. A. 6 Notions from 473 spectral theory. ) '" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BIBLIOGRAPHY . . . •. . . . . . . •. . . . . . . . . . . . . . . •. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Author: Gerd Grubb
Publisher:
ISBN: 9781461207702
Category :
Languages : en
Pages : 540
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Book Description
Author: G. Grubb
Publisher: Birkhäuser
ISBN: 9780817633493
Category : Science
Languages : en
Pages : 0
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Book Description
CHAPTER 1. STANDARD PSEUDO-DIFFERENTIAL BOUNDARY PROBLEMS AND THEIR REALIZATIONS 1. 1 Introductory remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1. 2 The calculus of pseudo-differential boundary problems . . •. 19 1. 3 Green's formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 1. 4 Realizations and normal boundary conditions . . . . . . . . . . . . . . 39 1. 5 Parameter-ellipticity and parabolicity . . . . . . . . . . . . . . . . . . . 50 1. 6 Adjoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 1. 7 Semiboundedness and coerciveness . . . . . . . . •. . . . . . . . . . . •. . . . 96 CHAPTER 2. THE CALCULUS OF PARAMETER-DEPENDENT OPERATORS 2. 1 Parameter-dependent pseudo-differential operators . . •. . . . . 125 2. 2 The transmission property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 2. 3 Parameter-dependent boundary symbol s . . . . . . . . . . . . . . . . . . . . . 179 2. 4 Operators and kernels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 2. 5 Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 2. 6 Composition of xn-independent boundary symbol operators . . 234 2. 7 Compositions in general . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 2. 8 Strictly homogeneous symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 CHAPTER 3. PARAMETRIX AND RESOLVENT CONSTRUCTIONS 3. 1 Ellipticity. Auxiliary elliptic operators . . . . . . . . . . . . . . . . 280 3. 2 The parametrix construction . . . . . . . . . . •. . . . . . . . . . . . . . . . . . . 297 3. 3 The resolvent of a realization . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 3. 4 Other special cases . . . . . . •. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 CHAPTER 4. SOME APPLICATIONS 4. 1 Evolution problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 4. 2 The heat operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 4. 3 An index formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 4. 4 Complex powers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 4. 5 Spectral asymptotics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 4. 6 Implicit eigenvalue problems . . . . . . . . . . . . . . . . . . . . . . . •. . . . . 437 4. 7 Singular perturbations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449 APPENDIX. VARIOUS PREREQUISITES (A. 1 General notation. A. 2 Functions and distributions. A. 3 Sobolev spaces. A. 4 Spaces over sub sets of mn. A. 5 Spaces over manifolds. A. 6 Notions from 473 spectral theory. ) '" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BIBLIOGRAPHY . . . •. . . . . . . •. . . . . . . . . . . . . . . •. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Author: G. Grubb
Publisher:
ISBN:
Category :
Languages : en
Pages : 12
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Author: Juan Gil
Publisher: Birkhäuser
ISBN: 3034878508
Category : Mathematics
Languages : en
Pages : 574
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Book Description
Boundary problems constitute an essential field of common mathematical interest, they lie in the center of research activities both in analysis and geometry. This book encompasses material from both disciplines, and focuses on their interactions which are particularly apparent in this field. Moreover, the survey style of the contributions makes the topics accessible to a broad audience with a background in analysis or geometry, and enables the reader to get a quick overview.
Author: M. Demuth
Publisher: Birkhäuser
ISBN: 3034886233
Category : Science
Languages : en
Pages : 355
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Book Description
Author: M. W. Wong
Publisher: Birkhäuser
ISBN: 3319475126
Category : Mathematics
Languages : en
Pages : 242
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Book Description
This volume consists of papers inspired by the special session on pseudo-differential operators at the 10th ISAAC Congress held at the University of Macau, August 3-8, 2015 and the mini-symposium on pseudo-differential operators in industries and technologies at the 8th ICIAM held at the National Convention Center in Beijing, August 10-14, 2015. The twelve papers included present cutting-edge trends in pseudo-differential operators and applications from the perspectives of Lie groups (Chapters 1-2), geometry (Chapters 3-5) and applications (Chapters 6-12). Many contributions cover applications in probability, differential equations and time-frequency analysis. A focus on the synergies of pseudo-differential operators with applications, especially real-life applications, enhances understanding of the analysis and the usefulness of these operators.
Author: Bert-Wolfgang Schulze
Publisher: Springer Science & Business Media
ISBN: 3034601980
Category : Mathematics
Languages : en
Pages : 294
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Book Description
Consists of the expository paper based on the 6-hour minicourse given by Professor Bert-Wolfgang Schulze, and sixteen papers based on lectures given at the workshop and on invitations.
Author: Niels Jacob
Publisher: Imperial College Press
ISBN: 1860945686
Category : Mathematics
Languages : en
Pages : 506
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Book Description
This work covers two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated.
