Distribution Integral Transforms and Applications
Title | Distribution Integral Transforms and Applications PDF eBook |
Author | Kierat |
Publisher | |
Pages | |
Release | |
Genre | |
ISBN | 9789056993191 |
Distribution, Integral Transforms and Applications
Title | Distribution, Integral Transforms and Applications PDF eBook |
Author | W. Kierat |
Publisher | CRC Press |
Pages | 162 |
Release | 2003-01-16 |
Genre | Mathematics |
ISBN | 9780415269582 |
The theory of distributions is most often presented as L. Schwartz originally presented it: as a theory of the duality of topological vector spaces. Although this is a sound approach, it can be difficult, demanding deep prior knowledge of functional analysis. The more elementary treatments that are available often consider distributions as limits of sequences of functions, but these usually present the theoretical foundations in a form too simplified for practical applications. Distributions, Integral Transforms and Applications offers an approachable introduction to the theory of distributions and integral transforms that uses Schwartz's description of distributions as linear continous forms on topological vector spaces. The authors use the theory of the Lebesgue integral as a fundamental tool in the proofs of many theorems and develop the theory from its beginnings to the point of proving many of the deep, important theorems, such as the Schwartz kernel theorem and the Malgrange-Ehrenpreis theorem. They clearly demonstrate how the theory of distributions can be used in cases such as Fourier analysis, when the methods of classical analysis are insufficient. Accessible to anyone who has completed a course in advanced calculus, this treatment emphasizes the remarkable connections between distributional theory, classical analysis, and the theory of differential equations and leads directly to applications in various branches of mathematics.
Distribution, Integral Transforms and Applications
Title | Distribution, Integral Transforms and Applications PDF eBook |
Author | W. Kierat |
Publisher | CRC Press |
Pages | 158 |
Release | 2003-01-16 |
Genre | Mathematics |
ISBN | 1482264811 |
The theory of distributions is most often presented as L. Schwartz originally presented it: as a theory of the duality of topological vector spaces. Although this is a sound approach, it can be difficult, demanding deep prior knowledge of functional analysis. The more elementary treatments that are available often consider distributions as limits o
Distributions, Fourier Transforms And Some Of Their Applications To Physics
Title | Distributions, Fourier Transforms And Some Of Their Applications To Physics PDF eBook |
Author | Schucker Thomas |
Publisher | World Scientific Publishing Company |
Pages | 180 |
Release | 1991-04-22 |
Genre | Science |
ISBN | 9813104406 |
In this book, distributions are introduced via sequences of functions. This approach due to Temple has two virtues:The Fourier transform is defined for functions and generalized to distributions, while the Green function is defined as the outstanding application of distributions. Using Fourier transforms, the Green functions of the important linear differential equations in physics are computed. Linear algebra is reviewed with emphasis on Hilbert spaces. The author explains how linear differential operators and Fourier transforms naturally fit into this frame, a point of view that leads straight to generalized fourier transforms and systems of special functions like spherical harmonics, Hermite, Laguerre, and Bessel functions.
Distributional Integral Transforms
Title | Distributional Integral Transforms PDF eBook |
Author | P. K. Banerji |
Publisher | |
Pages | 186 |
Release | 2005 |
Genre | Mathematics |
ISBN |
Integral Transforms and Their Applications
Title | Integral Transforms and Their Applications PDF eBook |
Author | Lokenath Debnath |
Publisher | CRC Press |
Pages | 723 |
Release | 2016-04-19 |
Genre | Mathematics |
ISBN | 1420010913 |
Keeping the style, content, and focus that made the first edition a bestseller, Integral Transforms and their Applications, Second Edition stresses the development of analytical skills rather than the importance of more abstract formulation. The authors provide a working knowledge of the analytical methods required in pure and applied mathematics, physics, and engineering. The second edition includes many new applications, exercises, comments, and observations with some sections entirely rewritten. It contains more than 500 worked examples and exercises with answers as well as hints to selected exercises. The most significant changes in the second edition include: New chapters on fractional calculus and its applications to ordinary and partial differential equations, wavelets and wavelet transformations, and Radon transform Revised chapter on Fourier transforms, including new sections on Fourier transforms of generalized functions, Poissons summation formula, Gibbs phenomenon, and Heisenbergs uncertainty principle A wide variety of applications has been selected from areas of ordinary and partial differential equations, integral equations, fluid mechanics and elasticity, mathematical statistics, fractional ordinary and partial differential equations, and special functions A broad spectrum of exercises at the end of each chapter further develops analytical skills in the theory and applications of transform methods and a deeper insight into the subject A systematic mathematical treatment of the theory and method of integral transforms, the book provides a clear understanding of the subject and its varied applications in mathematics, applied mathematics, physical sciences, and engineering.
Integral Transforms of Generalized Functions and Their Applications
Title | Integral Transforms of Generalized Functions and Their Applications PDF eBook |
Author | Ram Shankar Pathak |
Publisher | Routledge |
Pages | 432 |
Release | 2017-07-05 |
Genre | History |
ISBN | 135156269X |
For those who have a background in advanced calculus, elementary topology and functional analysis - from applied mathematicians and engineers to physicists - researchers and graduate students alike - this work provides a comprehensive analysis of the many important integral transforms and renders particular attention to all of the technical aspects of the subject. The author presents the last two decades of research and includes important results from other works.