Integral Transforms in Science and Engineering

1. Front Matter

   Pages i-xiii

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2. Finite-Dimensional Vector Spaces and the Fourier Transform

   1. Front Matter

      Pages 1-2

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   2. Concepts from Complex Vector Analysis and the Fourier Transform

      • Kurt Bernardo Wolf

      Pages 3-42

   3. The Application of Fourier Analysis to the Uncoupling of Lattices

      • Kurt Bernardo Wolf

      Pages 43-99

   4. Further Developments and Applications of the Finite Fourier Transform

      • Kurt Bernardo Wolf

      Pages 101-135

3. Fourier and Bessel Series

   1. Front Matter

      Pages 137-138

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   2. Function Vector Spaces and Fourier Series

      • Kurt Bernardo Wolf

      Pages 139-194

   3. Fourier Series in Diffusion and Wave Phenomena

      • Kurt Bernardo Wolf

      Pages 195-220

   4. Normal Mode Expansion and Bessel Series

      • Kurt Bernardo Wolf

      Pages 221-251

4. Fourier and Related Integral Transforms

   1. Front Matter

      Pages 253-254

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   2. Fourier Transforms

      • Kurt Bernardo Wolf

      Pages 255-332

   3. Integral Transforms Related to the Fourier Transform

      • Kurt Bernardo Wolf

      Pages 333-378

5. Canonical Transforms

   1. Front Matter

      Pages 379-379

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   2. Construction and Properties of Canonical Transforms

      • Kurt Bernardo Wolf

      Pages 381-416

   3. Applications to the Study of Differential Equations

      • Kurt Bernardo Wolf

      Pages 417-444

6. Back Matter

   Pages 445-489

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Integral transforms are among the main mathematical methods for the solution of equations describing physical systems, because, quite generally, the coupling between the elements which constitute such a system-these can be the mass points in a finite spring lattice or the continuum of a diffusive or elastic medium-prevents a straightforward "single-particle" solution. By describing the same system in an appropriate reference frame, one can often bring about a mathematical uncoupling of the equations in such a way that the solution becomes that of noninteracting constituents. The "tilt" in the reference frame is a finite or integral transform, according to whether the system has a finite or infinite number of elements. The types of coupling which yield to the integral transform method include diffusive and elastic interactions in "classical" systems as well as the more common quantum-mechanical potentials. The purpose of this volume is to present an orderly exposition of the theory and some of the applications of the finite and integral transforms associated with the names of Fourier, Bessel, Laplace, Hankel, Gauss, Bargmann, and several others in the same vein. The volume is divided into four parts dealing, respectively, with finite, series, integral, and canonical transforms. They are intended to serve as independent units. The reader is assumed to have greater mathematical sophistication in the later parts, though.

• Canon
• Finite
• Lattice
• Mathematica
• Volume
• equation
• form
• integral
• integral transform
• interaction
• system
• types

• Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, México D.F., México

  Kurt Bernardo Wolf

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