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The convolution transform includes as special cases such familiar
transforms as the Laplace, Fourier-sine, Fourier-cosine, Hankel,
Meier, and Weierstrass (or Gauss). As a consequence any general
theory about it may serve as a unifying influence for the
evergrowing literature concerning integral transforms. Originally
published in 1955. The Princeton Legacy Library uses the latest
print-on-demand technology to again make available previously
out-of-print books from the distinguished backlist of Princeton
University Press. These editions preserve the original texts of
these important books while presenting them in durable paperback
and hardcover editions. The goal of the Princeton Legacy Library is
to vastly increase access to the rich scholarly heritage found in
the thousands of books published by Princeton University Press
since its founding in 1905.
The convolution transform includes as special cases such familiar
transforms as the Laplace, Fourier-sine, Fourier-cosine, Hankel,
Meier, and Weierstrass (or Gauss). As a consequence any general
theory about it may serve as a unifying influence for the
evergrowing literature concerning integral transforms. Originally
published in 1955. The Princeton Legacy Library uses the latest
print-on-demand technology to again make available previously
out-of-print books from the distinguished backlist of Princeton
University Press. These editions preserve the original texts of
these important books while presenting them in durable paperback
and hardcover editions. The goal of the Princeton Legacy Library is
to vastly increase access to the rich scholarly heritage found in
the thousands of books published by Princeton University Press
since its founding in 1905.
In studies of general operators of the same nature, general
convolution transforms are immediately encountered as the objects
of inversion. The relation between differential operators and
integral transforms is the basic theme of this work, which is
geared toward upper-level undergraduates and graduate students. It
may be read easily by anyone with a working knowledge of real and
complex variable theory. Topics include the finite and non-finite
kernels, variation diminishing transforms, asymptotic behavior of
kernels, real inversion theory, representation theory, the
Weierstrass transform, and complex inversion theory.
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