Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators write by Nicolas Lerner. This book was released on 2011-01-30. Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators available in PDF, EPUB and Kindle. This book is devoted to the study of pseudo-di?erential operators, with special emphasis on non-selfadjoint operators, a priori estimates and localization in the phase space. We have tried here to expose the most recent developments of the theory with its applications to local solvability and semi-classical estimates for non-selfadjoint operators. The?rstchapter,Basic Notions of Phase Space Analysis,isintroductoryand gives a presentation of very classical classes of pseudo-di?erential operators, along with some basic properties. As an illustration of the power of these methods, we give a proof of propagation of singularities for real-principal type operators (using aprioriestimates,andnotFourierintegraloperators),andweintroducethereader to local solvability problems. That chapter should be useful for a reader, say at the graduate level in analysis, eager to learn some basics on pseudo-di?erential operators. The second chapter, Metrics on the Phase Space begins with a review of symplectic algebra, Wigner functions, quantization formulas, metaplectic group and is intended to set the basic study of the phase space. We move forward to the more general setting of metrics on the phase space, following essentially the basic assumptions of L. H ̈ ormander (Chapter 18 in the book [73]) on this topic.
Studies in Phase Space Analysis with Applications to PDEs
Studies in Phase Space Analysis with Applications to PDEs - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Studies in Phase Space Analysis with Applications to PDEs write by Massimo Cicognani. This book was released on 2013-03-12. Studies in Phase Space Analysis with Applications to PDEs available in PDF, EPUB and Kindle. This collection of original articles and surveys, emerging from a 2011 conference in Bertinoro, Italy, addresses recent advances in linear and nonlinear aspects of the theory of partial differential equations (PDEs). Phase space analysis methods, also known as microlocal analysis, have continued to yield striking results over the past years and are now one of the main tools of investigation of PDEs. Their role in many applications to physics, including quantum and spectral theory, is equally important. Key topics addressed in this volume include: *general theory of pseudodifferential operators *Hardy-type inequalities *linear and non-linear hyperbolic equations and systems *Schrödinger equations *water-wave equations *Euler-Poisson systems *Navier-Stokes equations *heat and parabolic equations Various levels of graduate students, along with researchers in PDEs and related fields, will find this book to be an excellent resource. Contributors T. Alazard P.I. Naumkin J.-M. Bony F. Nicola N. Burq T. Nishitani C. Cazacu T. Okaji J.-Y. Chemin M. Paicu E. Cordero A. Parmeggiani R. Danchin V. Petkov I. Gallagher M. Reissig T. Gramchev L. Robbiano N. Hayashi L. Rodino J. Huang M. Ruzhanky D. Lannes J.-C. Saut F. Linares N. Visciglia P.B. Mucha P. Zhang C. Mullaert E. Zuazua T. Narazaki C. Zuily
Pseudodifferential Operators with Automorphic Symbols
Pseudodifferential Operators with Automorphic Symbols - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Pseudodifferential Operators with Automorphic Symbols write by André Unterberger. This book was released on 2015-06-22. Pseudodifferential Operators with Automorphic Symbols available in PDF, EPUB and Kindle. The main results of this book combine pseudo differential analysis with modular form theory. The methods rely for the most part on explicit spectral theory and the extended use of special functions. The starting point is a notion of modular distribution in the plane, which will be new to most readers and relates under the Radon transformation to the classical one of modular form of the non-holomorphic type. Modular forms of the holomorphic type are addressed too in a more concise way, within a general scheme dealing with quantization theory and elementary, but novel, representation-theoretic concepts.
Advances in Microlocal and Time-Frequency Analysis
Advances in Microlocal and Time-Frequency Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Advances in Microlocal and Time-Frequency Analysis write by Paolo Boggiatto. This book was released on 2020-03-03. Advances in Microlocal and Time-Frequency Analysis available in PDF, EPUB and Kindle. The present volume gathers contributions to the conference Microlocal and Time-Frequency Analysis 2018 (MLTFA18), which was held at Torino University from the 2nd to the 6th of July 2018. The event was organized in honor of Professor Luigi Rodino on the occasion of his 70th birthday. The conference’s focus and the contents of the papers reflect Luigi’s various research interests in the course of his long and extremely prolific career at Torino University.
Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms
Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms write by André Unterberger. This book was released on 2011-08-06. Pseudodifferential Analysis, Automorphic Distributions in the Plane and Modular Forms available in PDF, EPUB and Kindle. Pseudodifferential analysis, introduced in this book in a way adapted to the needs of number theorists, relates automorphic function theory in the hyperbolic half-plane Π to automorphic distribution theory in the plane. Spectral-theoretic questions are discussed in one or the other environment: in the latter one, the problem of decomposing automorphic functions in Π according to the spectral decomposition of the modular Laplacian gives way to the simpler one of decomposing automorphic distributions in R2 into homogeneous components. The Poincaré summation process, which consists in building automorphic distributions as series of g-transforms, for g E SL(2;Z), of some initial function, say in S(R2), is analyzed in detail. On Π, a large class of new automorphic functions or measures is built in the same way: one of its features lies in an interpretation, as a spectral density, of the restriction of the zeta function to any line within the critical strip. The book is addressed to a wide audience of advanced graduate students and researchers working in analytic number theory or pseudo-differential analysis.
