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FOURIER ANALYSIS --- Moment problems (Mathematics) --- Exponential functions --- Control theory --- Distributed parameter systems --- Fourier analysis --- 517.98 --- Calculus, Operational --- Analysis, Fourier --- Mathematical analysis --- Functions, Exponential --- Hyperbolic functions --- Exponents (Algebra) --- Logarithms --- Transcendental functions --- Systems, Distributed parameter --- Engineering systems --- System analysis --- Dynamics --- Machine theory --- 517.98 Functional analysis and operator theory --- Functional analysis and operator theory

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This book deals with the concept of moments, and how they find application in subsurface hydrologic problems-particularly those dealing with solute transport. This book will be very valuable to researchers who are beginning to learn about moment analysis, and will also be of interest to advanced researchers as well. Both temporal and spatial moments are dealt with in some detail for a wide variety of problems. Several examples using experimental data, both from laboratory columns and field experiments, are provided to give the readers a clear idea about the scope of this method. Apart from conventional uses of moments for solute transport problems, this book contains chapters dealing with use of moments in interval computing, vapour phase transport applications, transfer functions to subsurface tile drains, and construction of breakthrough curves from knowledge of moments.

Soils --- Transformations (Mathematics) --- Moment problems (Mathematics) --- Solute movement. --- Calculus, Operational --- Algorithms --- Differential invariants --- Geometry, Differential --- Movement of solutes in soils --- Soil physics --- Hydraulic engineering. --- Differential equations, partial. --- Geography. --- Hydrogeology. --- Hydrology/Water Resources. --- Partial Differential Equations. --- Earth Sciences, general. --- Cosmography --- Earth sciences --- World history --- Partial differential equations --- Engineering, Hydraulic --- Engineering --- Fluid mechanics --- Hydraulics --- Shore protection --- Hydrology. --- Partial differential equations. --- Earth sciences. --- Geosciences --- Environmental sciences --- Physical sciences --- Aquatic sciences --- Hydrography --- Water --- Geohydrology --- Geology --- Hydrology --- Groundwater

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The origins of Schur analysis lie in a 1917 article by Issai Schur in which he constructed a numerical sequence to correspond to a holomorphic contractive function on the unit disk. These sequences are now known as Schur parameter sequences. Schur analysis has grown significantly since its beginnings in the early twentieth century and now encompasses a wide variety of problems related to several classes of holomorphic functions and their matricial generalizations. These problems include interpolation and moment problems as well as Schur parametrization of particular classes of contractive or nonnegative Hermitian block matrices. This book is primarily devoted to topics related to matrix versions of classical interpolation and moment problems. The major themes include Schur analysis of nonnegative Hermitian block Hankel matrices and the construction of Schur-type algorithms. This book also covers a number of recent developments in orthogonal rational matrix functions, matrix-valued Carathéodory functions and maximal weight solutions for particular matricial moment problems on the unit circle.

Differential equations -- Numerical solutions. --- Differential equations. --- Integral equations -- Numerical solutions. --- Interpolation --- Schur functions --- Inverse problems (Differential equations) --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Applied Mathematics --- Calculus --- Interpolation. --- Schur functions. --- Moment problems (Mathematics) --- S-functions --- Schur's functions --- Mathematics. --- Functions of complex variables. --- Integral transforms. --- Operational calculus. --- Operator theory. --- Operator Theory. --- Integral Transforms, Operational Calculus. --- Functions of a Complex Variable. --- Calculus, Operational --- Holomorphic functions --- Approximation theory --- Numerical analysis --- Integral Transforms. --- Complex variables --- Elliptic functions --- Functions of real variables --- Transform calculus --- Integral equations --- Transformations (Mathematics) --- Functional analysis --- Operational calculus --- Differential equations --- Electric circuits

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Continued fractions --- Functions, Orthogonal --- Moment problems (Mathematics) --- 517.52 --- 517.58 --- 517.52 Series and sequences --- Series and sequences --- Calculus, Operational --- Fractions, Continued --- Series --- Processes, Infinite --- Orthogonal functions --- Fourier analysis --- Series, Orthogonal --- 517.58 Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- Mathematical analysis --- Numerical approximation theory