Download or read book Locally Convex Spaces and Linear Partial Differential Equations written by François Treves and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is hardly an exaggeration to say that, if the study of general topolog ical vector spaces is justified at all, it is because of the needs of distribu tion and Linear PDE * theories (to which one may add the theory of convolution in spaces of hoi om orphic functions). The theorems based on TVS ** theory are generally of the "foundation" type: they will often be statements of equivalence between, say, the existence - or the approx imability -of solutions to an equation Pu = v, and certain more "formal" properties of the differential operator P, for example that P be elliptic or hyperboJic, together with properties of the manifold X on which P is defined. The latter are generally geometric or topological, e. g. that X be P-convex (Definition 20. 1). Also, naturally, suitable conditions will have to be imposed upon the data, the v's, and upon the stock of possible solutions u. The effect of such theorems is to subdivide the study of an equation like Pu = v into two quite different stages. In the first stage, we shall look for the relevant equivalences, and if none is already available in the literature, we shall try to establish them. The second stage will consist of checking if the "formal" or "geometric" conditions are satisfied.
Download or read book Locally Convex Spaces and Linear Partial Differential Equations written by Khayr al-Din al- Tunisi and published by . This book was released on 1967 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Locally convex spaces and linear partial differential equations written by François Trèves and published by . This book was released on 1967 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear Partial Differential Equations written by Francois Treves and published by CRC Press. This book was released on 1970-01-01 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers existence and approximation theorems in functional analysis, L-squared inequalities, necessary and sufficient conditions for existence of solutions (variable coefficients), and L-squared estimates and pseudo-convexity. Includes further reading and bibliographic references.
Download or read book Topological Vector Spaces Distributions and Kernels written by François Treves and published by Elsevier. This book was released on 2016-06-03 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological Vector Spaces, Distributions and Kernels discusses partial differential equations involving spaces of functions and space distributions. The book reviews the definitions of a vector space, of a topological space, and of the completion of a topological vector space. The text gives examples of Frechet spaces, Normable spaces, Banach spaces, or Hilbert spaces. The theory of Hilbert space is similar to finite dimensional Euclidean spaces in which they are complete and carry an inner product that can determine their properties. The text also explains the Hahn-Banach theorem, as well as the applications of the Banach-Steinhaus theorem and the Hilbert spaces. The book discusses topologies compatible with a duality, the theorem of Mackey, and reflexivity. The text describes nuclear spaces, the Kernels theorem and the nuclear operators in Hilbert spaces. Kernels and topological tensor products theory can be applied to linear partial differential equations where kernels, in this connection, as inverses (or as approximations of inverses), of differential operators. The book is suitable for vector mathematicians, for students in advanced mathematics and physics.
Download or read book Linear Partial Differential Equations with Constant Coefficients written by Francois Treves and published by CRC Press. This book was released on 1966 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Existence and approximation theorems for general differential operators -- General L2 estimates -- Fundamental solutions -- The approximation theorem -- Existence theorems for differential operators with constant coefficients -- Convexity with respect to a differential polynomial -- Interior regularity of solutions -- Partial hypoellipticity -- Existence and approximation theorems in spaces of analytic functions -- Appendix A. Semi-algebraic sets -- Appendix B. On uniqueness in the Cauchy problem -- Appendix C. Some formulas of non-commutative algebra.
Download or read book Transmutation and Operator Differential Equations written by and published by Elsevier. This book was released on 1979-01-01 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transmutation and Operator Differential Equations
Download or read book Functional Analysis Sobolev Spaces and Partial Differential Equations written by Haim Brezis and published by Springer Science & Business Media. This book was released on 2010-11-02 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.
Download or read book Analytically Uniform Spaces and Their Applications to Convolution Equations written by C. A. Berenstein and published by Springer. This book was released on 2006-11-14 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Notions of Convexity written by Lars Hörmander and published by Springer Science & Business Media. This book was released on 2007-06-25 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first two chapters of this book are devoted to convexity in the classical sense, for functions of one and several real variables respectively. This gives a background for the study in the following chapters of related notions which occur in the theory of linear partial differential equations and complex analysis such as (pluri-)subharmonic functions, pseudoconvex sets, and sets which are convex for supports or singular supports with respect to a differential operator. In addition, the convexity conditions which are relevant for local or global existence of holomorphic differential equations are discussed.
Download or read book Partial Differential and Integral Equations written by Heinrich Begehr and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of the Proceedings of the congress ISAAC '97 collects the con tributions of the four sections 1. Function theoretic and functional analytic methods for pde, 2. Applications of function theory of several complex variables to pde, 3. Integral equations and boundary value problems, 4. Partial differential equations. Most but not all of the authors have participated in the congress. Unfortunately some from Eastern Europe and Asia have not managed to come because of lack of financial support. Nevertheless their manuscripts of the proposed talks are included in this volume. The majority of the papers deal with complex methods. Among them boundary value problems in particular the Riemann-Hilbert, the Riemann (Hilbert) and related problems are treated. Boundary behaviour of vector-valued functions are studied too. The Riemann-Hilbert problem is solved for elliptic complex equations, for mixed complex equations, and for several complex variables. It is considered in a general topological setting for mappings into q;n and related to Toeplitz operators. Convolution operators are investigated for nilpotent Lie groups leading to some consequences for the null space of the tangential Cauchy Riemann operator. Some boundary value problems for overdetermined systems in balls of q;n are solved explicitly. A survey is given for the Gauss-Manin connection associated with deformations of curve singularities. Several papers deal with generalizations of analytic functions with various applications to mathematical physics. Singular integrals in quaternionic anal ysis are studied which are applied to the time-harmonic Maxwell equations.
Download or read book Solution Sets of Differential Equations in Abstract Spaces written by Robert Dragoni and published by CRC Press. This book was released on 1996-04-03 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents results on the geometric/topological structure of the solution set S of an initial-value problem x(t) = f(t, x(t)), x(0) =xo, when f is a continuous function with values in an infinite-dimensional space. A comprehensive survey of existence results and the properties of S, e.g. when S is a connected set, a retract, an acyclic set, is presented. The authors also survey results onthe properties of S for initial-value problems involving differential inclusions, and for boundary-value problems. This book will be of particular interest to researchers in ordinary and partial differential equations and some workers in control theory.
Download or read book Lecture Notes on Functional Analysis written by Alberto Bressan and published by American Mathematical Soc.. This book was released on 2013 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is addressed to graduate students in mathematics or other disciplines who wish to understand the essential concepts of functional analysis and their applications to partial differential equations. The book is intentionally concise, presenting all the fundamental concepts and results but omitting the more specialized topics. Enough of the theory of Sobolev spaces and semigroups of linear operators is included as needed to develop significant applications to elliptic, parabolic, and hyperbolic PDEs. Throughout the book, care has been taken to explain the connections between theorems in functional analysis and familiar results of finite-dimensional linear algebra. The main concepts and ideas used in the proofs are illustrated with a large number of figures. A rich collection of homework problems is included at the end of most chapters. The book is suitable as a text for a one-semester graduate course.
Download or read book Reflexive Spaces of Smooth Functions written by Marie Kerjean and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Around the curry-coward correspondence, proof-theory has grown along two distinct fields : the theory of programming languages, for which formulas acts as data types, and the semantic study of proofs. The latter consists in giving mathematical models of proofs and programs. In particular, denotational semantics distinguishes data types which serves as input or output of programs, and allows in return for a finer understanding of proofs and programs. Linear Logic (LL) gives a logical interpretation of the basic notions from/of linear algebra, while Differential Linear Logic allows for a logical understanding of differentiation. This manuscript strengthens the link between proof-theory and functional analysis, and highlights the role of linear involutive negation in DiLL. The first part of this thesis consists in a quick overview of prerequisites on the notions of linearity, polarisation and differentiation in proof-theory, and gives the necessary background in the theory of locally convex topological vector spaces. The second part uses two classic topologies on the dual of a topological vector space and gives two models of DiLL: the weak topology allows only for a discrete interpretation of proofs through formal power series, while the Mackey topology on the dual allows for a smooth and polarised model of DiLL. Finally, the third part interprets proofs of DiLL by distributions. We detail a polarized model of DiLL in which negatives are Fréchet Nuclear spaces, and proofs are distributions with compact support. We also show that solving linear partial differential equations with constant coefficients can be typed by a syntax similar to the one of DiLL, which we detail.
Download or read book The Cauchy Problem for Higher Order Abstract Differential Equations written by Ti-Jun Xiao and published by Springer. This book was released on 2013-12-11 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this book is to present the basic theory and some recent de velopments concerning the Cauchy problem for higher order abstract differential equations u(n)(t) + ~ AiU(i)(t) = 0, t ~ 0, { U(k)(O) = Uk, 0 ~ k ~ n-l. where AQ, Ab . . . , A - are linear operators in a topological vector space E. n 1 Many problems in nature can be modeled as (ACP ). For example, many n initial value or initial-boundary value problems for partial differential equations, stemmed from mechanics, physics, engineering, control theory, etc. , can be trans lated into this form by regarding the partial differential operators in the space variables as operators Ai (0 ~ i ~ n - 1) in some function space E and letting the boundary conditions (if any) be absorbed into the definition of the space E or of the domain of Ai (this idea of treating initial value or initial-boundary value problems was discovered independently by E. Hille and K. Yosida in the forties). The theory of (ACP ) is closely connected with many other branches of n mathematics. Therefore, the study of (ACPn) is important for both theoretical investigations and practical applications. Over the past half a century, (ACP ) has been studied extensively.
Download or read book Geometry Of Pdes And Mechanics written by Agostino Prastaro and published by World Scientific. This book was released on 1996-06-20 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the theory of partial differential equations (PDEs) from a modern geometric point of view so that PDEs can be characterized by using either technique of differential geometry or algebraic geometry. This allows us to recognize the richness of the structure of PDEs. It presents, for the first time, a geometric theory of non-commutative (quantum) PDEs and gives a general application of this theory to quantum field theory and quantum supergravity.
Download or read book Differential Equations on Measures and Functional Spaces written by Vassili Kolokoltsov and published by Springer. This book was released on 2019-06-20 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced book focuses on ordinary differential equations (ODEs) in Banach and more general locally convex spaces, most notably the ODEs on measures and various function spaces. It briefly discusses the fundamentals before moving on to the cutting edge research in linear and nonlinear partial and pseudo-differential equations, general kinetic equations and fractional evolutions. The level of generality chosen is suitable for the study of the most important nonlinear equations of mathematical physics, such as Boltzmann, Smoluchovskii, Vlasov, Landau-Fokker-Planck, Cahn-Hilliard, Hamilton-Jacobi-Bellman, nonlinear Schroedinger, McKean-Vlasov diffusions and their nonlocal extensions, mass-action-law kinetics from chemistry. It also covers nonlinear evolutions arising in evolutionary biology and mean-field games, optimization theory, epidemics and system biology, in general models of interacting particles or agents describing splitting and merging, collisions and breakage, mutations and the preferential-attachment growth on networks. The book is intended mainly for upper undergraduate and graduate students, but is also of use to researchers in differential equations and their applications. It particularly highlights the interconnections between various topics revealing where and how a particular result is used in other chapters or may be used in other contexts, and also clarifies the links between the languages of pseudo-differential operators, generalized functions, operator theory, abstract linear spaces, fractional calculus and path integrals.
