Classical Microlocal Analysis In The Space Of Hyperfunctions
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Classical Microlocal Analysis In The Space Of Hyperfunctions
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Author : Seiichiro Wakabayashi
language : en
Publisher: Springer
Release Date : 2007-05-06
Classical Microlocal Analysis In The Space Of Hyperfunctions written by Seiichiro Wakabayashi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-06 with Mathematics categories.
The book develops "Classical Microlocal Analysis" in the spaces of hyperfunctions and microfunctions, which makes it possible to apply the methods in the distribution category to the studies on partial differential equations in the hyperfunction category. Here "Classical Microlocal Analysis" means that it does not use "Algebraic Analysis." The main tool in the text is, in some sense, integration by parts. The studies on microlocal uniqueness, analytic hypoellipticity and local solvability are reduced to the problems to derive energy estimates (or a priori estimates). The author assumes basic understanding of theory of pseudodifferential operators in the distribution category.
Singularities Of Integrals
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Author : Frédéric Pham
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-22
Singularities Of Integrals written by Frédéric Pham and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-22 with Mathematics categories.
Bringing together two fundamental texts from Frédéric Pham’s research on singular integrals, the first part of this book focuses on topological and geometrical aspects while the second explains the analytic approach. Using notions developed by J. Leray in the calculus of residues in several variables and R. Thom’s isotopy theorems, Frédéric Pham’s foundational study of the singularities of integrals lies at the interface between analysis and algebraic geometry, culminating in the Picard-Lefschetz formulae. These mathematical structures, enriched by the work of Nilsson, are then approached using methods from the theory of differential equations and generalized from the point of view of hyperfunction theory and microlocal analysis. Providing a ‘must-have’ introduction to the singularities of integrals, a number of supplementary references also offer a convenient guide to the subjects covered. This book will appeal to both mathematicians and physicists with an interest in the area of singularities of integrals. Frédéric Pham, now retired, was Professor at the University of Nice. He has published several educational and research texts. His recent work concerns semi-classical analysis and resurgent functions.
Consistency Problems For Heath Jarrow Morton Interest Rate Models
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Author : Damir Filipovic
language : en
Publisher: Springer
Release Date : 2004-11-02
Consistency Problems For Heath Jarrow Morton Interest Rate Models written by Damir Filipovic and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-02 with Mathematics categories.
Bond markets differ in one fundamental aspect from standard stock markets. While the latter are built up to a finite number of trade assets, the underlying basis of a bond market is the entire term structure of interest rates: an infinite-dimensional variable which is not directly observable. On the empirical side, this necessitates curve-fitting methods for the daily estimation of the term structure. Pricing models, on the other hand, are usually built upon stochastic factors representing the term structure in a finite-dimensional state space. Written for readers with knowledge in mathematical finance (in particular interest rate theory) and elementary stochastic analysis, this research monograph has threefold aims: to bring together estimation methods and factor models for interest rates, to provide appropriate consistency conditions and to explore some important examples.
Forward Backward Stochastic Differential Equations And Their Applications
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Author : Jin Ma
language : en
Publisher: Springer
Release Date : 2007-04-24
Forward Backward Stochastic Differential Equations And Their Applications written by Jin Ma and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-24 with Mathematics categories.
This volume is a survey/monograph on the recently developed theory of forward-backward stochastic differential equations (FBSDEs). Basic techniques such as the method of optimal control, the 'Four Step Scheme', and the method of continuation are presented in full. Related topics such as backward stochastic PDEs and many applications of FBSDEs are also discussed in detail. The volume is suitable for readers with basic knowledge of stochastic differential equations, and some exposure to the stochastic control theory and PDEs. It can be used for researchers and/or senior graduate students in the areas of probability, control theory, mathematical finance, and other related fields.
The Method Of Approximate Inverse Theory And Applications
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Author : Thomas Schuster
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-07
The Method Of Approximate Inverse Theory And Applications written by Thomas Schuster and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-07 with Mathematics categories.
Inverse problems arise whenever one tries to calculate a required quantity from given measurements of a second quantity that is associated to the first one. Besides medical imaging and non-destructive testing, inverse problems also play an increasing role in other disciplines such as industrial and financial mathematics. Hence, there is a need for stable and efficient solvers. The book is concerned with the method of approximate inverse which is a regularization technique for stably solving inverse problems in various settings such as L2-spaces, Hilbert spaces or spaces of distributions. The performance and functionality of the method is demonstrated on several examples from medical imaging and non-destructive testing such as computerized tomography, Doppler tomography, SONAR, X-ray diffractometry and thermoacoustic computerized tomography. The book addresses graduate students and researchers interested in the numerical analysis of inverse problems and regularization techniques or in efficient solvers for the applications mentioned above.
Construction Of Global Lyapunov Functions Using Radial Basis Functions
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Author : Peter Giesl
language : en
Publisher: Springer
Release Date : 2007-04-11
Construction Of Global Lyapunov Functions Using Radial Basis Functions written by Peter Giesl and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-11 with Mathematics categories.
The basin of attraction of an equilibrium of an ordinary differential equation can be determined using a Lyapunov function. A new method to construct such a Lyapunov function using radial basis functions is presented in this volume intended for researchers and advanced students from both dynamical systems and radial basis functions. Besides an introduction to both areas and a detailed description of the method, it contains error estimates and many examples.
Sharp Real Part Theorems
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Author : Gershon Kresin
language : en
Publisher: Springer
Release Date : 2007-03-05
Sharp Real Part Theorems written by Gershon Kresin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-05 with Mathematics categories.
This volume contains a coherent point of view on various sharp pointwise inequalities for analytic functions in a disk in terms of the real part of the function on the boundary circle or in the disk itself. Inequalities of this type are frequently used in the theory of entire functions and in the analytic number theory.
Deformations Of Singularities
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Author : Jan Stevens
language : en
Publisher: Springer
Release Date : 2003-01-01
Deformations Of Singularities written by Jan Stevens and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
These notes deal with deformation theory of complex analytic singularities and related objects. The first part treats general theory. The central notion is that of versal deformation in several variants. The theory is developed both in an abstract way and in a concrete way suitable for computations. The second part deals with more specific problems, specially on curves and surfaces. Smoothings of singularities are the main concern. Examples are spread throughout the text.
Mathematical Foundation Of Turbulent Viscous Flows
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Author : Peter Constantin
language : en
Publisher: Springer
Release Date : 2005-11-24
Mathematical Foundation Of Turbulent Viscous Flows written by Peter Constantin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-24 with Mathematics categories.
Constantin presents the Euler equations of ideal incompressible fluids and the blow-up problem for the Navier-Stokes equations of viscous fluids, describing major mathematical questions of turbulence theory. These are connected to the Caffarelli-Kohn-Nirenberg theory of singularities for the incompressible Navier-Stokes equations, explained in Gallavotti's lectures. Kazhikhov introduces the theory of strong approximation of weak limits via the method of averaging, applied to Navier-Stokes equations. Y. Meyer focuses on nonlinear evolution equations and related unexpected cancellation properties, either imposed on the initial condition, or satisfied by the solution itself, localized in space or in time variable. Ukai discusses the asymptotic analysis theory of fluid equations, the Cauchy-Kovalevskaya technique for the Boltzmann-Grad limit of the Newtonian equation, the multi-scale analysis, giving compressible and incompressible limits of the Boltzmann equation, and the analysis of their initial layers.
Topology Of Singular Fibers Of Differentiable Maps
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Author : Osamu Saeki
language : en
Publisher: Springer
Release Date : 2004-08-30
Topology Of Singular Fibers Of Differentiable Maps written by Osamu Saeki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-30 with Mathematics categories.
The volume develops a thorough theory of singular fibers of generic differentiable maps. This is the first work that establishes the foundational framework of the global study of singular differentiable maps of negative codimension from the viewpoint of differential topology. The book contains not only a general theory, but also some explicit examples together with a number of very concrete applications. This is a very interesting subject in differential topology, since it shows a beautiful interplay between the usual theory of singularities of differentiable maps and the geometric topology of manifolds.