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Multivariate polysplines are a new mathematical technique that has arisen from a synthesis of approximation theory and the theory of partial differential equations. It is an invaluable means to interpolate practical data with smooth functions.Multivariate polysplines have applications in the design of surfaces and ""smoothing"" that are essential in computer aided geometric design (CAGD and CAD/CAM systems), geophysics, magnetism, geodesy, geography, wavelet analysis and signal and image processing. In many cases involving practical data in these areas, polysplines are proving more effecti
Spline theory. --- Polyharmonic functions. --- Differential equations, Elliptic --- Numerical solutions. --- Functions, Polyharmonic --- Harmonic functions --- Potential theory (Mathematics) --- Spline functions --- Approximation theory --- Interpolation --- Polyharmonic functions --- Spline theory --- Numerical solutions
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This monograph provides an introduction and a survey of recent results in potential theory with respect to the Laplace-Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn. Topics covered include Poisson-Szegö integrals on the ball, the Green's function for D and the Riesz decomposition theorem for invariant subharmonic functions. The extension to the ball of the classical Fatou theorem on non-tangible limits of Poisson integrals, and Littlewood's theorem on the existence of radial limits of subharmonic functions are covered in detail. The monograph also contains recent results on admissible and tangential boundary limits of Green potentials, and Lp inequalities for the invariant gradient of Green potentials. Applications of some of the results to Hp spaces, and weighted Bergman and Dirichlet spaces of invariant harmonic functions are included. The notes are self-contained, and should be accessible to anyone with some basic knowledge of several complex variables.
Invariants. --- Potential theory (Mathematics) --- Unit ball. --- Ball, Unit --- Holomorphic functions --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics
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Equilibrium and nonequilibrium properties of correlated many-body systems are of growing interest in many areas of physics, including condensed matter, dense plasmas, nuclear matter and particles. The most powerful and general method which is equally applied to all these areas is given by quantum field theory. This book provides an overview of the basic ideas and concepts of the method of nonequilibrium Green's functions, written by the leading experts and presented in a way accessible to non-specialists and graduate students. It is complemented by invited review papers on modern applications
Green's functions --- Many-body problem --- Quantum theory --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics)
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In this book an account of the growth theory of subharmonic functions is given, which is directed towards its applications to entire functions of one and several complex variables. The presentation aims at converting the noble art of constructing an entire function with prescribed asymptotic behaviour to a handicraft. For this one should only construct the limit set that describes the asymptotic behaviour of the entire function. All necessary material is developed within the book, hence it will be most useful as a reference book for the construction of entire functions.
Electronic books. -- local. --- Potential theory (Mathematics). --- Subharmonic functions. --- Subharmonic functions --- Operations Research --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Potential theory (Mathematics) --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Functions, Subharmonic --- Mathematics. --- Potential Theory. --- Mathematical analysis --- Mechanics --- Functions of real variables
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Markov processes and potential theory
Markov processes. --- Potential theory (Mathematics) --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Stochastic processes
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This third volume of the monograph examines potential theory. The first chapter develops potential theory with respect to a single kernel (or discrete time semigroup). All the essential ideas of the theory are presented: excessive functions, reductions, sweeping, maximum principle. The second chapter begins with a study of the notion of reduction in the most general situation possible - the ``gambling house'' of Dubins and Savage. The beautiful results presented have never been made accessible to a wide public. These are then connected with the theory of sweeping with respect to a cone of cont
Probabilities. --- Potential theory (Mathematics) --- Semigroups. --- Group theory --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk
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Potential theory is the broad area of mathematical analysis encompassing such topics as harmonic and subharmonic functions, the Dirichlet problem, harmonic measure, Green's functions, potentials and capacity. This is an introduction to the subject suitable for beginning graduate students, concentrating on the important case of two dimensions. This permits a simpler treatment than other books, yet is still sufficient for a wide range of applications to complex analysis; these include Picard's theorem, the Phragmén-Lindelöf principle, the Koebe one-quarter mapping theorem and a sharp quantitative form of Runge's theorem. In addition there is a chapter on connections with functional analysis and dynamical systems, which shows how the theory can be applied to other parts of mathematics, and gives a flavour of some recent research. Exercises are provided throughout, enabling the book to be used with advanced courses on complex analysis or potential theory.
Potential theory (Mathematics) --- Functions of complex variables. --- Complex variables --- Elliptic functions --- Functions of real variables --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Functions of complex variables --- Functions (Mathematics)
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This text bridges the gap between the classic texts on potential theory and modern books on applied geophysics. It opens with an introduction to potential theory, emphasising those aspects particularly important to earth scientists, such as Laplace's equation, Newtonian potential, magnetic and electrostatic fields, and conduction of heat. The theory is then applied to the interpretation of gravity and magnetic anomalies, drawing on examples from modern geophysical literature. Topics explored include regional and global fields, forward modeling, inverse methods, depth-to-source estimation, ideal bodies, analytical continuation, and spectral analysis. The book includes numerous exercises and a variety of computer subroutines written in FORTRAN. Graduate students and researchers in geophysics will find this book essential.
Geophysics --- Potential theory (Mathematics) --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Geological physics --- Terrestrial physics --- Earth sciences --- Physics --- Technique. --- 550.3 --- 550.3 Geophysics
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In this volume two topics are discussed: the construction of Feller and Lp-sub-Markovian semigroups by starting with a pseudo-differential operator, and the potential theory of these semigroups and their generators. The first part of the text essentially discusses the analysis of pseudo-differential operators with negative definite symbols and develops a symbolic calculus; in addition, it deals with special approaches, such as subordination in the sense of Bochner. The second part handles capacities, function spaces associated with continuous negative definite functions, Lp -sub-Markovian sem
Semigroups of operators. --- Pseudodifferential operators. --- Potential theory (Mathematics) --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Operators, Pseudodifferential --- Pseudo-differential operators --- Operator theory --- Operators, Semigroups of
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Green's functions represent one of the classical and widely used issues in the area of differential equations. This monograph is looking at applied elliptic and parabolic type partial differential equations in two variables. The elliptic type includes the Laplace, static Klein-Gordon and biharmonic equation. The parabolic type is represented by the classical heat equation and the Black-Scholes equation which has emerged as a mathematical model in financial mathematics. The book is attractive for practical needs: It contains many easily computable or computer friendly representations of Green's functions, includes all the standard Green's functions and many novel ones, and provides innovative and new approaches that might lead to Green's functions. The book is a useful source for everyone who is studying or working in the fields of science, finance, or engineering that involve practical solution of partial differential equations.
Green's functions. --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- Elliptic. --- Green's Function. --- Parabolic. --- Partial Differential Equation.
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