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Author: Wilhelm Kecs
Publisher:
ISBN:
Category : Convolutions (Mathematics)
Languages : en
Pages : 321
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Book Description
Author: Wilhelm Kecs
Publisher:
ISBN:
Category : Convolutions (Mathematics)
Languages : en
Pages : 321
Get Book Here
Book Description
Author: W. Kecs
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 360
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Book Description
As a result of the important properties it possesses, the convolution product holds a central place among the various modes of function composition. The extension of the convolution product in the distribution space created a natural framework for the growth and enrichment of its properties, and it is due to this fact that the operation has become a powerful mathematical tool in symbolic calculus, distribution approximation, Fourier series, and the solution of boundary value problems. The high effectiveness of this mathematical operation is especially reflected in its properties with respect to the Fourier and Laplace transforms and in the description of the solutions to linear differential equations with constant coefficients. The aim of this work is to systematically present the fundamental properties of the convolution product for functions and distributions. Additionally, it is shown how the method is used in the study of mathematical physics, deformable solids, mechanical systems, electrical circuits, etc. --Back cover.
Author: Hari M. Srivastava
Publisher: Springer Science & Business Media
ISBN: 9401580928
Category : Mathematics
Languages : en
Pages : 259
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Book Description
This volume presents a state-of-the-art account of the theory and applications of integral equations of convolution type, and of certain classes of integro-differential and non-linear integral equations. An extensive and well-motivated discussion of some open questions and of various important directions for further research is also presented. The book has been written so as to be self-contained, and includes a list of symbols with their definitions. For users of convolution integral equations, the volume contains numerous, well-classified inversion tables which correspond to the various convolutions and intervals of integration. It also has an extensive, up-to-date bibliography. The convolution integral equations which are considered arise naturally from a large variety of physical situations and it is felt that the types of solutions discussed will be usefull in many diverse disciplines of applied mathematics and mathematical physical. For researchers and graduate students in the mathematical and physical sciences whose work involves the solution of integral equations.
Author: Bjoern Sundt
Publisher: Springer Science & Business Media
ISBN: 3540929002
Category : Mathematics
Languages : en
Pages : 348
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Book Description
Since 1980, methods for recursive evaluation of aggregate claims distributions have received extensive attention in the actuarial literature. This book gives a unified survey of the theory and is intended to be self-contained to a large extent. As the methodology is applicable also outside the actuarial field, it is presented in a general setting, but actuarial applications are used for motivation. The book is divided into two parts. Part I is devoted to univariate distributions, whereas in Part II, the methodology is extended to multivariate settings. Primarily intended as a monograph, this book can also be used as text for courses on the graduate level. Suggested outlines for such courses are given. The book is of interest for actuaries and statisticians working within the insurance and finance industry, as well as for people in other fields like operations research and reliability theory.
Author: Wilhelm Kecs
Publisher:
ISBN:
Category :
Languages : en
Pages : 332
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Book Description
Author: Lei Guan
Publisher: Springer
ISBN: 3319520008
Category : Technology & Engineering
Languages : en
Pages : 166
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Book Description
This book presents essential perspectives on digital convolutions in wireless communications systems and illustrates their corresponding efficient real-time field-programmable gate array (FPGA) implementations. FPGAs or generic all programmable devices will soon become widespread, serving as the “brains” of all types of real-time smart signal processing systems, like smart networks, smart homes and smart cities. The book examines digital convolution by bringing together the following main elements: the fundamental theory behind the mathematical formulae together with corresponding physical phenomena; virtualized algorithm simulation together with benchmark real-time FPGA implementations; and detailed, state-of-the-art case studies on wireless applications, including popular linear convolution in digital front ends (DFEs); nonlinear convolution in digital pre-distortion (DPD) enabled high-efficiency wireless RF transceivers; and fast linear convolution in massive multiple-input multiple-output (MIMO) systems. After reading this book, students and professionals will be able to: · Understand digital convolution with inside-out information: discover what convolution is, why it is important and how it works. · Enhance their FPGA design skills, i.e., enhance their FPGA-related prototyping capability with model-based hands-on examples. · Rapidly expand their digital signal processing (DSP) blocks: to examine how to rapidly and efficiently create (DSP) functional blocks on a programmable FPGA chip as a reusable intellectual property (IP) core. · Upgrade their expertise as both “thinkers” and “doers”: minimize/close the gap between mathematical equations and FPGA implementations for existing and emerging wireless applications.
Author: Karlheinz Spindler
Publisher: Routledge
ISBN: 135146924X
Category : Mathematics
Languages : en
Pages : 554
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Book Description
A comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.
Author: A. Uglanov
Publisher: Springer Science & Business Media
ISBN: 9401596220
Category : Mathematics
Languages : en
Pages : 280
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Book Description
It seems hard to believe, but mathematicians were not interested in integration problems on infinite-dimensional nonlinear structures up to 70s of our century. At least the author is not aware of any publication concerning this theme, although as early as 1967 L. Gross mentioned that the analysis on infinite dimensional manifolds is a field of research with rather rich opportunities in his classical work [2. This prediction was brilliantly confirmed afterwards, but we shall return to this later on. In those days the integration theory in infinite dimensional linear spaces was essentially developed in the heuristic works of RP. Feynman [1], I. M. Gelfand, A. M. Yaglom [1]). The articles of J. Eells [1], J. Eells and K. D. Elworthy [1], H. -H. Kuo [1], V. Goodman [1], where the contraction of a Gaussian measure on a hypersurface, in particular, was built and the divergence theorem (the Gauss-Ostrogradskii formula) was proved, appeared only in the beginning of the 70s. In this case a Gaussian specificity was essential and it was even pointed out in a later monograph of H. -H. Kuo [3] that the surface measure for the non-Gaussian case construction problem is not simple and has not yet been solved. A. V. Skorokhod [1] and the author [6,10] offered different approaches to such a construction. Some other approaches were offered later by Yu. L. Daletskii and B. D. Maryanin [1], O. G. Smolyanov [6], N. V.
Author: Naum I︠A︡kovlevich Vilenkin
Publisher: Springer Science & Business Media
ISBN: 9780792332107
Category : Mathematics
Languages : en
Pages : 528
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Book Description
The present book is a continuation of the three-volume work Representation of Lie Groups and Special Functions by the same authors. Here, they deal with the exposition of the main new developments in the contemporary theory of multivariate special functions, bringing together material that has not been presented in monograph form before. The theory of orthogonal symmetric polynomials (Jack polynomials, Macdonald's polynomials and others) and multivariate hypergeometric functions associated to symmetric polynomials are treated. Multivariate hypergeometric functions, multivariate Jacobi polynomials and h-harmonic polynomials connected with root systems and Coxeter groups are introduced. Also, the theory of Gel'fand hypergeometric functions and the theory of multivariate hypergeometric series associated to Clebsch-Gordan coefficients of the unitary group U(n) is given. The volume concludes with an extensive bibliography. For research mathematicians and physicists, postgraduate students in mathematics and mathematical and theoretical physics.
Author: Albrecht Böttcher
Publisher: Birkhäuser
ISBN: 3034881525
Category : Mathematics
Languages : en
Pages : 464
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Book Description
Many problems of the engineering sciences, physics, and mathematics lead to con volution equations and their various modifications. Convolution equations on a half-line can be studied by having recourse to the methods and results of the theory of Toeplitz and Wiener-Hopf operators. Convolutions by integrable kernels have continuous symbols and the Cauchy singular integral operator is the most prominent example of a convolution operator with a piecewise continuous symbol. The Fredholm theory of Toeplitz and Wiener-Hopf operators with continuous and piecewise continuous (matrix) symbols is well presented in a series of classical and recent monographs. Symbols beyond piecewise continuous symbols have discontinuities of oscillating type. Such symbols emerge very naturally. For example, difference operators are nothing but convolution operators with almost periodic symbols: the operator defined by (A
