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On the Generalized Hankel and K Transformations
Published online by Cambridge University Press: 20 November 2018
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The K transformation (also called the Meijer transformation) has been extended by Zemanian [1; 2] to a class of generalized functions, For , he defined the K transform of f by
(1)
In [2, Section 6.6] the following inversion theorem for the K transform of f is proven:
(2)
in the sense of weak convergence in D'(I). Here, σ is any fixed real number greater than σf, μ is zero or a complex number with positive real part and D'f(I) is the space of Schwartz distributions on I = (0, ∞).
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- Copyright © Canadian Mathematical Society 1969
References
1.
Zemanian, A.H., A distributional K transformation. J. Soc. Ind. Appl. Math.
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Weiss, L., On the foundation of transfer function analysis. Int. J. Eng. Sc.
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Koh, E. L. and Zemanian, A.H., The complex Hankel and I-transformations of generalized functions. J. Soc. Ind. Appl. Math.
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Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F.G., Higher transcendental functions, Vol. II. (McGraw-Hill, New York, 1953).Google Scholar
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