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Book
Hilbert's programs and beyond
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ISBN: 9780195372229 9780199707157 0195372220 0199707154 Year: 2013 Publisher: New York, N.Y. Oxford University Press

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Presents the foundational work of David Hilbert in a sequence of thematically organized essays. They first trace the roots of Hilbert's work to the radical transformation of mathematics in the 19th century and bring out his pivotal role in creating mathematicallogic and proof theory. They then analyze techniques and results of "classical" proof theory as well as their dramatic expansion in modern proof theory. This intellectual experience finally opens horizons for reflection on the nature of mathematics in the 21st century: Sieg articulates his position of reductive structuralism and explores mathematical capacities via computational models.


Book
The Sine-Gordon equation in the semiclassical limit : dynamics of fluxon condensates
Authors: ---
ISBN: 1470410591 Year: 2013 Publisher: Providence, Rhode Island : American Mathematical Society,

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Book
The Sine-Gordon equation in the semiclassical limit : dynamics of fluxon condensates
Authors: ---
ISBN: 9780821885451 Year: 2013 Publisher: Providence, R.I. American Mathematical Society


Book
Multivariate Characteristic and Correlation Functions
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ISSN: 01790986 ISBN: 3110223996 9783110223996 9783110223989 3110223988 Year: 2013 Volume: 50 Publisher: Berlin Boston

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In a certain sense characteristic functions and correlation functions are the same, the common underlying concept is positive definiteness. Many results in probability theory, mathematical statistics and stochastic processes can be derived by using these functions. While there are books on characteristic functions of one variable, books devoting some sections to the multivariate case, and books treating the general case of locally compact groups, interestingly there is no book devoted entirely to the multidimensional case which is extremely important for applications. This book is intended to fill this gap at least partially. It makes the basic concepts and results on multivariate characteristic and correlation functions easily accessible to both students and researchers in a comprehensive manner. The first chapter presents basic results and should be read carefully since it is essential for the understanding of the subsequent chapters. The second chapter is devoted to correlation functions, their applications to stationary processes and some connections to harmonic analysis. In Chapter 3 we deal with several special properties, Chapter 4 is devoted to the extension problem while Chapter 5 contains a few applications. A relatively large appendix comprises topics like infinite products, functional equations, special functions or compact operators.


Book
Spectral theory and its applications
Author:
ISBN: 9781139505727 9781107032309 9781107471672 9781139626095 1139626094 1139505726 9781139611213 1139611216 9781139613071 1139613073 110703230X 1107238021 1107254981 113961679X 1283899493 1139622374 Year: 2013 Volume: 139 Publisher: Cambridge : Cambridge University Press,

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Bernard Helffer's graduate-level introduction to the basic tools in spectral analysis is illustrated by numerous examples from the Schrödinger operator theory and various branches of physics: statistical mechanics, superconductivity, fluid mechanics and kinetic theory. The later chapters also introduce non self-adjoint operator theory with an emphasis on the role of the pseudospectra. The author's focus on applications, along with exercises and examples, enables readers to connect theory with practice so that they develop a good understanding of how the abstract spectral theory can be applied. The final chapter provides various problems that have been the subject of active research in recent years and will challenge the reader's understanding of the material covered.


Book
Hilbert space methods in signal processing
Authors: ---
ISBN: 9780511844515 9781107010031 0511844514 9781107336452 1107336457 9781299773059 1299773052 9781107333130 110733313X 9781107334793 1107334799 1107010039 1107234638 1107332419 1107326699 1107335620 9781107234635 9781107332416 9781107326699 9781107335622 Year: 2013 Publisher: Cambridge : Cambridge University Press,

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This lively and accessible book describes the theory and applications of Hilbert spaces and also presents the history of the subject to reveal the ideas behind theorems and the human struggle that led to them. The authors begin by establishing the concept of 'countably infinite', which is central to the proper understanding of separable Hilbert spaces. Fundamental ideas such as convergence, completeness and dense sets are first demonstrated through simple familiar examples and then formalised. Having addressed fundamental topics in Hilbert spaces, the authors then go on to cover the theory of bounded, compact and integral operators at an advanced but accessible level. Finally, the theory is put into action, considering signal processing on the unit sphere, as well as reproducing kernel Hilbert spaces. The text is interspersed with historical comments about central figures in the development of the theory, which helps bring the subject to life.


Book
Three classes of nonlinear stochastic partial differential equations
Author:
ISBN: 981445236X 9789814452366 9789814452359 9814452351 1299651844 9781299651845 Year: 2013 Publisher: [Hackensack] New Jersey

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The study of measure-valued processes in random environments has seen some intensive research activities in recent years whereby interesting nonlinear stochastic partial differential equations (SPDEs) were derived. Due to the nonlinearity and the non-Lipschitz continuity of their coefficients, new techniques and concepts have recently been developed for the study of such SPDEs. These include the conditional Laplace transform technique, the conditional mild solution, and the bridge between SPDEs and some kind of backward stochastic differential equations. This volume provides an introduction to


Book
Elliptic Curves, Hilbert Modular Forms and Galois Deformations
Authors: --- --- --- --- --- et al.
ISBN: 3034806175 3034806183 Year: 2013 Publisher: Basel : Springer Basel : Imprint: Birkhäuser,

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The notes in this volume correspond to advanced courses held at the Centre de Recerca Matemàtica as part of the research program in Arithmetic Geometry in the 2009-2010 academic year. The notes by Laurent Berger provide an introduction to p-adic Galois representations and Fontaine rings, which are especially useful for describing many local deformation rings at p that arise naturally in Galois deformation theory. The notes by Gebhard Böckle offer a comprehensive course on Galois deformation theory, starting from the foundational results of Mazur and discussing in detail the theory of pseudo-representations and their deformations, local deformations at places l ≠ p and local deformations at p which are flat. In the last section,the results of Böckle and Kisin on presentations of global deformation rings over local ones are discussed. The notes by Mladen Dimitrov present the basics of the arithmetic theory of Hilbert modular forms and varieties, with an emphasis on the study of the images of the attached Galois representations, on modularity lifting theorems over totally real number fields, and on the cohomology of Hilbert modular varieties with integral coefficients.  The notes by Lassina Dembélé and John Voight describe methods for performing explicit computations in spaces of Hilbert modular forms. These methods depend on the Jacquet-Langlands correspondence and on computations in spaces of quaternionic modular forms, both for the case of definite and indefinite quaternion algebras. Several examples are given, and applications to modularity of Galois representations are discussed.  The notes by Tim Dokchitser describe the proof, obtained by the author in a joint project with Vladimir Dokchitser, of the parity conjecture for elliptic curves over number fields under the assumption of finiteness of the Tate-Shafarevich group. The statement of the Birch and Swinnerton-Dyer conjecture is included, as well as a detailed study of local and global root numbers of elliptic curves and their classification.


Book
Spectral/hp element methods for computational fluid dynamics
Authors: ---
ISBN: 142942205X 0191523798 9786610753970 1280753978 9780191523793 Year: 2013 Publisher: Oxford

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This edition includes new material on discontinuous Galerkin methods, non-tensorial nodal spectral element methods in simplex domains, and stabilisation and filtering techniques.

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