Global and Local Regularity of Fourier Integral Operators on Weighted and Unweighted Spaces - 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 Global and Local Regularity of Fourier Integral Operators on Weighted and Unweighted Spaces write by David Dos Santos Ferreira. This book was released on 2014-04-07. Global and Local Regularity of Fourier Integral Operators on Weighted and Unweighted Spaces available in PDF, EPUB and Kindle. The authors investigate the global continuity on spaces with of Fourier integral operators with smooth and rough amplitudes and/or phase functions subject to certain necessary non-degeneracy conditions. In this context they prove the optimal global boundedness result for Fourier integral operators with non-degenerate phase functions and the most general smooth Hörmander class amplitudes i.e. those in with . They also prove the very first results concerning the continuity of smooth and rough Fourier integral operators on weighted spaces, with and (i.e. the Muckenhoupt weights) for operators with rough and smooth amplitudes and phase functions satisfying a suitable rank condition.
Global and Local Regularity of Fourier Integral Operators on Weighted and Unweighted Spaces
Global and Local Regularity of Fourier Integral Operators on Weighted and Unweighted Spaces - 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 Global and Local Regularity of Fourier Integral Operators on Weighted and Unweighted Spaces write by David Dos Santos Ferreira. This book was released on 2014-10-03. Global and Local Regularity of Fourier Integral Operators on Weighted and Unweighted Spaces available in PDF, EPUB and Kindle.
To an Effective Local Langlands Correspondence
To an Effective Local Langlands Correspondence - 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 To an Effective Local Langlands Correspondence write by Colin J. Bushnell. This book was released on 2014-08-12. To an Effective Local Langlands Correspondence available in PDF, EPUB and Kindle. Let F be a non-Archimedean local field. Let \mathcal{W}_{F} be the Weil group of F and \mathcal{P}_{F} the wild inertia subgroup of \mathcal{W}_{F}. Let \widehat {\mathcal{W}}_{F} be the set of equivalence classes of irreducible smooth representations of \mathcal{W}_{F}. Let \mathcal{A}^{0}_{n}(F) denote the set of equivalence classes of irreducible cuspidal representations of \mathrm{GL}_{n}(F) and set \widehat {\mathrm{GL}}_{F} = \bigcup _{n\ge 1} \mathcal{A}^{0}_{n}(F). If \sigma \in \widehat {\mathcal{W}}_{F}, let ^{L}{\sigma }\in \widehat {\mathrm{GL}}_{F} be the cuspidal representation matched with \sigma by the Langlands Correspondence. If \sigma is totally wildly ramified, in that its restriction to \mathcal{P}_{F} is irreducible, the authors treat ^{L}{\sigma} as known. From that starting point, the authors construct an explicit bijection \mathbb{N}:\widehat {\mathcal{W}}_{F} \to \widehat {\mathrm{GL}}_{F}, sending \sigma to ^{N}{\sigma}. The authors compare this "naïve correspondence" with the Langlands correspondence and so achieve an effective description of the latter, modulo the totally wildly ramified case. A key tool is a novel operation of "internal twisting" of a suitable representation \pi (of \mathcal{W}_{F} or \mathrm{GL}_{n}(F)) by tame characters of a tamely ramified field extension of F, canonically associated to \pi. The authors show this operation is preserved by the Langlands correspondence.
Index Theory for Locally Compact Noncommutative Geometries
Index Theory for Locally Compact Noncommutative Geometries - 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 Index Theory for Locally Compact Noncommutative Geometries write by A. L. Carey. This book was released on 2014-08-12. Index Theory for Locally Compact Noncommutative Geometries available in PDF, EPUB and Kindle. Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, the authors prove the local index formula for spectral triples over nonunital algebras, without the assumption of local units in our algebra. This formula has been successfully used to calculate index pairings in numerous noncommutative examples. The absence of any other effective method of investigating index problems in geometries that are genuinely noncommutative, particularly in the nonunital situation, was a primary motivation for this study and the authors illustrate this point with two examples in the text. In order to understand what is new in their approach in the commutative setting the authors prove an analogue of the Gromov-Lawson relative index formula (for Dirac type operators) for even dimensional manifolds with bounded geometry, without invoking compact supports. For odd dimensional manifolds their index formula appears to be completely new.
Wave Packet Analysis of Feynman Path Integrals
Wave Packet Analysis of Feynman Path Integrals - 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 Wave Packet Analysis of Feynman Path Integrals write by Fabio Nicola. This book was released on 2022-07-28. Wave Packet Analysis of Feynman Path Integrals available in PDF, EPUB and Kindle. The purpose of this monograph is to offer an accessible and essentially self-contained presentation of some mathematical aspects of the Feynman path integral in non-relativistic quantum mechanics. In spite of the primary role in the advancement of modern theoretical physics and the wide range of applications, path integrals are still a source of challenging problem for mathematicians. From this viewpoint, path integrals can be roughly described in terms of approximation formulas for an operator (usually the propagator of a Schrödinger-type evolution equation) involving a suitably designed sequence of operators. In keeping with the spirit of harmonic analysis, the guiding theme of the book is to illustrate how the powerful techniques of time-frequency analysis - based on the decomposition of functions and operators in terms of the so-called Gabor wave packets – can be successfully applied to mathematical path integrals, leading to remarkable results and paving the way to a fruitful interaction. This monograph intends to build a bridge between the communities of people working in time-frequency analysis and mathematical/theoretical physics, and to provide an exposition of the present novel approach along with its basic toolkit. Having in mind a researcher or a Ph.D. student as reader, we collected in Part I the necessary background, in the most suitable form for our purposes, following a smooth pedagogical pattern. Then Part II covers the analysis of path integrals, reflecting the topics addressed in the research activity of the authors in the last years.
