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In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank
Functional analysis --- Functional analysis. --- Analyse fonctionnelle. --- Analyse fonctionnelle --- ELSEVIER-B EPUB-LIV-FT --- 517.98 --- 517.98 Functional analysis and operator theory --- Functional analysis and operator theory --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations
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This is the only book that deals comprehensively with fixed point theorems throughout mathematics. Their importance is due, as the book demonstrates, to their wide applicability. Beyond the first chapter, each of the other seven can be read independently of the others so the reader has much flexibility to follow his/her own interests. The book is written for graduate students and professional mathematicians and could be of interest to physicists, economists and engineers --
Fixed point theory. --- Fixed point theorems (Topology) --- Nonlinear operators --- Coincidence theory (Mathematics) --- Fixed point theory --- 517.98 --- 517.98 Functional analysis and operator theory --- Functional analysis and operator theory --- Point fixe, Théorème du. --- Point fixe, Théorème du.
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This monograph only requires of the reader a basic knowledge of classical analysis: measure theory, analytic functions, Hilbert spaces, functional analysis. The book is self-contained, except for a few technical tools, for which precise references are given.Part I starts with finite-dimensional spaces and general spectral theory. But very soon (Chapter III), new material is presented, leading to new directions for research. Open questions are mentioned here. Part II concerns compactness and its applications, not only spectral theory for compact operators (Invariant Subspaces and Lomono
Analytical spaces --- Operator theory --- Invariant subspaces. --- Operator theory. --- Invariant subspaces --- #KVIV:BB --- 517.98 --- 517.98 Functional analysis and operator theory --- Functional analysis and operator theory --- Functional analysis --- Subspaces, Invariant --- Hilbert space
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Applications of functional analysis and operator theory
Functional analysis. --- Operator theory. --- Functional calculus --- Functional analysis --- Calculus of variations --- Functional equations --- Integral equations --- Operator theory --- 517.98 --- 517.98 Functional analysis and operator theory --- Functional analysis and operator theory --- Analyse fonctionnelle --- Espaces linéaires normés --- Normed linear spaces --- Espaces linéaires normés. --- Théorie des opérateurs --- ELSEVIER-B EPUB-LIV-FT --- Équations aux dérivées partielles --- Opérateurs, Théorie des
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Functional analysis has become a sufficiently large area of mathematics that it is possible to find two research mathematicians, both of whom call themselves functional analysts, who have great difficulty understanding the work of the other. The common thread is the existence of a linear space with a topology or two (or more). Here the paths diverge in the choice of how that topology is defined and in whether to study the geometry of the linear space, or the linear operators on the space, or both. In this book I have tried to follow the common thread rather than any special topic. I have included some topics that a few years ago might have been thought of as specialized but which impress me as interesting and basic. Near the end of this work I gave into my natural temptation and included some operator theory that, though basic for operator theory, might be considered specialized by some functional analysts.
Functional analysis --- Functional analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- 517.98 --- 517.98 Functional analysis and operator theory --- Functional analysis and operator theory --- Analyse fonctionnelle --- Global analysis (Mathematics). --- Analysis. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical analysis. --- Analysis (Mathematics). --- 517.1 Mathematical analysis --- Mathematical analysis
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Graph Theory has proved to be an extremely useful tool for solving combinatorial problems in such diverse areas as Geometry, Algebra, Number Theory, Topology, Operations Research and Optimization. It is natural to attempt to generalise the concept of a graph, in order to attack additional combinatorial problems. The idea of looking at a family of sets from this standpoint took shape around 1960. In regarding each set as a ``generalised edge'' and in calling the family itself a ``hypergraph'', the initial idea was to try to extend certain classical results of Graph Theory such as the theorems o
Discrete mathematics --- Hypergraphs. --- Graph theory. --- Hypergraphs --- 517.98 --- 681.3*G22 --- 517.98 Functional analysis and operator theory --- Functional analysis and operator theory --- Graph theory --- 681.3*G22 Graph theory: graph algorithms; network problems; path and tree problems; trees--See also {681.3*F22} --- Graph theory: graph algorithms; network problems; path and tree problems; trees--See also {681.3*F22} --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Extremal problems
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In this book we are concerned with the study of a certain class of in?nite matrices and two important properties of them: their Fredholmness and the stability of the approximation by their ?nite truncations. Let us take these two properties as a starting point for the big picture that shall be presented in what follows. Stability Fredholmness We think of our in?nite matrices as bounded linear operators on a Banach space E of two-sided in?nite sequences. Probably the simplest case to start with 2 +? is the space E = of all complex-valued sequences u=(u ) for which m m=?? 2 |u | is summable over m? Z. m Theclassofoperatorsweareinterestedinconsistsofthoseboundedandlinear operatorsonE whichcanbeapproximatedintheoperatornormbybandmatrices. We refer to them as band-dominated operators. Of course, these considerations 2 are not limited to the space E = . We will widen the selection of the underlying space E in three directions: p • We pass to the classical sequence spaces with 1? p??. n • Our elements u=(u )? E have indices m? Z rather than just m? Z. m • We allow values u in an arbitrary ?xed Banach spaceX rather than C.
Infinite matrices. --- Linear operators. --- Numerical analysis. --- Integral equations. --- Matrices infinies --- Opérateurs linéaires --- Analyse numérique --- Equations intégrales --- Infinite matrices. » More like this Linear operators. » More like this Numerical analysis. » More like this Integral equations. --- Infinite matrices --- Linear operators --- Numerical analysis --- Integral equations --- Algebra --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- 517.98 --- Functional analysis and operator theory --- 517.98 Functional analysis and operator theory --- Equations, Integral --- Matrices, Infinite --- Linear maps --- Maps, Linear --- Operators, Linear --- Mathematics. --- Matrix theory. --- Algebra. --- Functional analysis. --- Functional Analysis. --- Linear and Multilinear Algebras, Matrix Theory. --- Numerical Analysis. --- Mathematical analysis --- Operator theory --- Functional equations --- Functional analysis --- Matrices --- Functional calculus --- Calculus of variations
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Uniquely, this book presents a coherent, concise and unified way of combining elements from two distinct “worlds,” functional analysis (FA) and partial differential equations (PDEs), and is intended for students who have a good background in real analysis. This text presents a smooth transition from FA to PDEs by analyzing in great detail the simple case of one-dimensional PDEs (i.e., ODEs), a more manageable approach for the beginner. Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Moreover, the wealth of exercises and additional material presented, leads the reader to the frontier of research. This book has its roots in a celebrated course taught by the author for many years and is a completely revised, updated, and expanded English edition of the important “Analyse Fonctionnelle” (1983). Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English version is a welcome addition to this list. The first part of the text deals with abstract results in FA and operator theory. The second part is concerned with the study of spaces of functions (of one or more real variables) having specific differentiability properties, e.g., the celebrated Sobolev spaces, which lie at the heart of the modern theory of PDEs. The Sobolev spaces occur in a wide range of questions, both in pure and applied mathematics, appearing in linear and nonlinear PDEs which arise, for example, in differential geometry, harmonic analysis, engineering, mechanics, physics etc. and belong in the toolbox of any graduate student studying analysis.
Differential equations, Partial. --- Functional analysis. --- Sobolev spaces. --- Sobolev spaces --- Sobolev, Espaces de --- Partial differential equations: difference methods elliptic equations finite element methods hyperbolic equations method of lines parabolic equations (Numerical analysis) --- 681.3 *G18 Partial differential equations: difference methods elliptic equations finite element methods hyperbolic equations method of lines parabolic equations (Numerical analysis) --- Spaces, Sobolev --- Mathematics. --- Difference equations. --- Functional equations. --- Partial differential equations. --- Functional Analysis. --- Partial Differential Equations. --- Difference and Functional Equations. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Partial differential equations --- Equations, Functional --- Functional analysis --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Math --- Science --- Differential equations, Partial --- 517.95 --- 517.98 --- 681.3*G18 --- Function spaces --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 517.95 Partial differential equations --- 517.98 Functional analysis and operator theory --- Functional analysis and operator theory --- Analytical spaces --- 681.3 *G18 --- Analyse fonctionnelle --- Equations aux dérivées partielles --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Differential equations, partial. --- Analyse fonctionnelle. --- Équations aux dérivées partielles. --- Sobolev, Espaces de.
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