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Author : Roy A. Sorensen
Publisher : Routledge
Page : 304 pages
File Size : 40,6 Mb
Release : 2002-01-22
Category : Philosophy
ISBN : 9781134868520
First published in 1993. Routledge is an imprint of Taylor & Francis, an informa company.
Author : Roy A. Sorensen
Publisher : Routledge
Page : 304 pages
File Size : 42,5 Mb
Release : 2002-01-22
Category : Philosophy
ISBN : 9781134868537
First published in 1993. Routledge is an imprint of Taylor & Francis, an informa company.
Author : G. Grubb
Publisher : Springer Science & Business Media
Page : 520 pages
File Size : 55,6 Mb
Release : 2013-03-09
Category : Science
ISBN : 9781475718980
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 : Alex Kaltenbach
Publisher : Springer Nature
Page : 364 pages
File Size : 55,9 Mb
Release : 2023-09-12
Category : Mathematics
ISBN : 9783031296703
This book provides a comprehensive analysis of the existence of weak solutions of unsteady problems with variable exponents. The central motivation is the weak solvability of the unsteady p(.,.)-Navier–Stokes equations describing the motion of an incompressible electro-rheological fluid. Due to the variable dependence of the power-law index p(.,.) in this system, the classical weak existence analysis based on the pseudo-monotone operator theory in the framework of Bochner–Lebesgue spaces is not applicable. As a substitute for Bochner–Lebesgue spaces, variable Bochner–Lebesgue spaces are introduced and analyzed. In the mathematical framework of this substitute, the theory of pseudo-monotone operators is extended to unsteady problems with variable exponents, leading to the weak solvability of the unsteady p(.,.)-Navier–Stokes equations under general assumptions. Aimed primarily at graduate readers, the book develops the material step-by-step, starting with the basics of PDE theory and non-linear functional analysis. The concise introductions at the beginning of each chapter, together with illustrative examples, graphics, detailed derivations of all results and a short summary of the functional analytic prerequisites, will ease newcomers into the subject.
Author : Rudolf Carnap
Publisher : Open Court Publishing
Page : 402 pages
File Size : 43,5 Mb
Release : 2003
Category : Philosophy
ISBN : 0812695232
Available for the first time in 20 years, here are two important works from the 1920s by the best-known representative of the Vienna Circle. In The Logical Structure of the World, Carnap adopts the position of "methodological solipsism" and shows that it is possible to describe the world from the immediate data of experience. In his Pseudoproblems in Philosophy, he asserts that many philosophical problems are meaningless.
Author : M. W. Wong,Hongmei Zhu
Publisher : Birkhäuser
Page : 239 pages
File Size : 46,5 Mb
Release : 2017-01-20
Category : Mathematics
ISBN : 9783319475127
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 : Luigi Rodino,Bert-Wolfgang Schulze,Man Wah Wong
Publisher : American Mathematical Soc.
Page : 432 pages
File Size : 47,9 Mb
Release : 2007-11-21
Category : Mathematics
ISBN : 0821871552
This volume is based on lectures given at the workshop on pseudo-differential operators held at the Fields Institute from December 11, 2006 to December 15, 2006. The two main themes of the workshop and hence this volume are partial differential equations and time-frequency analysis. The contents of this volume consist of five mini-courses for graduate students and post-docs, and fifteen papers on related topics. Of particular interest in this volume are the mathematical underpinnings, applications and ramifications of the relatively new Stockwell transform, which is a hybrid of the Gabor transform and the wavelet transform. The twenty papers in this volume reflect modern trends in the development of pseudo-differential operators.
Author : Massimo Pigliucci,Maarten Boudry
Publisher : University of Chicago Press
Page : 479 pages
File Size : 46,7 Mb
Release : 2013-08-16
Category : Science
ISBN : 9780226051826
“A remarkable contribution to one of the most vexing problems in science: the ‘demarcation’ problem, or how to distinguish science from nonscience.” —Francisco J. Ayala, author of Darwin’s Gift to Science and Religion What sets the practice of rigorously tested, sound science apart from pseudoscience? In this volume, the contributors seek to answer this question, known to philosophers of science as “the demarcation problem.” This issue has a long history in philosophy, stretching as far back as the early twentieth century and the work of Karl Popper. But by the late 1980s, scholars in the field began to treat the demarcation problem as impossible to solve and futile to ponder. However, the essays that Massimo Pigliucci and Maarten Boudry have assembled in this volume make a rousing case for the unequivocal importance of reflecting on the separation between pseudoscience and sound science. Moreover, the demarcation problem is not a purely theoretical dilemma of mere academic interest: it affects parents’ decisions to vaccinate children and governments’ willingness to adopt policies that prevent climate change. Pseudoscience often mimics science, using the superficial language and trappings of actual scientific research to seem more respectable. Even a well-informed public can be taken in by such questionable theories dressed up as science. Pseudoscientific beliefs compete with sound science on the health pages of newspapers for media coverage and in laboratories for research funding. Now more than ever the ability to separate genuine scientific findings from spurious ones is vital, and The Philosophy of Pseudoscience provides ground for philosophers, sociologists, historians, and laypeople to make decisions about what science is or isn’t. “A manual to overcome our natural cognitive biases.” —Corriere della Sera (Italy)
Author : Yuri I. Karlovich,Luigi Rodino,Bernd Silbermann,Ilya M. Spitkovsky
Publisher : Springer Science & Business Media
Page : 410 pages
File Size : 46,9 Mb
Release : 2012-10-30
Category : Mathematics
ISBN : 9783034805377
This volume is a collection of papers devoted to the 70th birthday of Professor Vladimir Rabinovich. The opening article (by Stefan Samko) includes a short biography of Vladimir Rabinovich, along with some personal recollections and bibliography of his work. It is followed by twenty research and survey papers in various branches of analysis (pseudodifferential operators and partial differential equations, Toeplitz, Hankel, and convolution type operators, variable Lebesgue spaces, etc.) close to Professor Rabinovich's research interests. Many of them are written by participants of the International workshop “Analysis, Operator Theory, and Mathematical Physics” (Ixtapa, Mexico, January 23–27, 2012) having a long history of scientific collaboration with Vladimir Rabinovich, and are partially based on the talks presented there.The volume will be of great interest to researchers and graduate students in differential equations, operator theory, functional and harmonic analysis, and mathematical physics.
Author : Heinz O. Cordes,Bernhard Gramsch,Harold Widom
Publisher : Springer
Page : 495 pages
File Size : 48,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540478867
Author : Sabir Umarov
Publisher : Springer
Page : 434 pages
File Size : 54,6 Mb
Release : 2015-08-18
Category : Mathematics
ISBN : 9783319207711
The book systematically presents the theories of pseudo-differential operators with symbols singular in dual variables, fractional order derivatives, distributed and variable order fractional derivatives, random walk approximants, and applications of these theories to various initial and multi-point boundary value problems for pseudo-differential equations. Fractional Fokker-Planck-Kolmogorov equations associated with a large class of stochastic processes are presented. A complex version of the theory of pseudo-differential operators with meromorphic symbols based on the recently introduced complex Fourier transform is developed and applied for initial and boundary value problems for systems of complex differential and pseudo-differential equations.
Author : Stevan Pilipović,Joachim Toft
Publisher : Birkhäuser
Page : 290 pages
File Size : 43,9 Mb
Release : 2015-04-27
Category : Mathematics
ISBN : 9783319146188
This book gathers peer-reviewed contributions representing modern trends in the theory of generalized functions and pseudo-differential operators. It is dedicated to Professor Michael Oberguggenberger (Innsbruck University, Austria) in honour of his 60th birthday. The topics covered were suggested by the ISAAC Group in Generalized Functions (GF) and the ISAAC Group in Pseudo-Differential Operators (IGPDO), which met at the 9th ISAAC congress in Krakow, Poland in August 2013. Topics include Columbeau algebras, ultra-distributions, partial differential equations, micro-local analysis, harmonic analysis, global analysis, geometry, quantization, mathematical physics, and time-frequency analysis. Featuring both essays and research articles, the book will be of great interest to graduate students and researchers working in analysis, PDE and mathematical physics, while also offering a valuable complement to the volumes on this topic previously published in the OT series.
Author : Luigi Rodino,M. W. Wong,Hongmei Zhu
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 51,9 Mb
Release : 2011-03-14
Category : Mathematics
ISBN : 9783034800495
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.
Author : Beatrix Himmelmann,Robert Louden
Publisher : Walter de Gruyter GmbH & Co KG
Page : 286 pages
File Size : 48,5 Mb
Release : 2015-09-25
Category : Philosophy
ISBN : 9783110366396
What reasons do we have to be moral, and are these reasons more compelling than the reasons we have to pursue non-moral projects? Ever since the Sophists first raised this question, it has been a focal point of debate. Why be Moral? is a collection of new essays on this fundamental philosophical problem, written by an international team of leading scholars in the field.
Author : Bert-Wolfgang Schulze,M. W. Wong
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 53,9 Mb
Release : 2010-03-01
Category : Mathematics
ISBN : 9783034601986
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.