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On the Theory of Vector Valued Fourier Hyperfunctions

On the Theory of Vector Valued Fourier Hyperfunctions
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Edge of the Wedge Theorem for Fourier Hyperfunctions

Edge of the Wedge Theorem for Fourier Hyperfunctions
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Schwartz kernel theorem for the Fourier hyperfunctions

Schwartz kernel theorem for the Fourier hyperfunctions
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Periodic Hyperfunctions and Fourier Series Fourier Series

Mathematics and Its Application Japanese Series, 1992
We have now almost finished the general discussion of hyperfunctions. From now on we shall attempt to apply this general theory to various cases. In this chapter we study periodic hyperfunctions. Then we shall see that the theory of Fourier series is naturally absorbed into the theory of Fourier transformations.
Isao Imai, Imai Isao
exaly   +2 more sources

Fourier analysis, distributions and hyperfunctions

Integral Transforms and Special Functions, 1998
The theory of hyperfunctions and Fourier hyperfunctions is a really natural extension of the Schwartz theory of distributions and tempered distributions. We show that the naturalness of hyperfunctions comparing our results in hyperfunctions and the corresponding results in distributions in such areas as the characterization of test function spaces in ...
Soon-Yeong Chung, Dohan Kim, Jaeyoung Chung   +2 more
exaly   +2 more sources

Analytic fourier hyperfunctions

Applicable Analysis, 1999
It is proved first a generalized Painleve's theorem to be used to prove necessary and sufficient conditions that a Fourier hyperfunction is defined by a real analytic function. These results are applied to the Taylor asymptotic expansion for Fourier hyperfunctions.
Bogoljub Stanković
exaly   +2 more sources

The structure of a convergent family of fourier hyperfunctions

Integral Transforms and Special Functions, 1998
We give the structural properties of a family of Fourier hyper-functions which converges as . The main result is also given in [5] but here we give an extended version with all the details of the proofs.
B Stanković
exaly   +2 more sources

Generalized Fourier expansion in kernels of convolution operators on Fourier hyperfunctions

Analysis (Germany), 2007
We prove that the kernels of surjective convolution operators on Fourier hyperfunctions (and on Fourier ultra-hyperfunctions) admit a basis of exponential solutions. The corresponding coefficient spaces are explicitly determined.
Michael Langenbruch
exaly   +3 more sources

Asymptotic Taylor expansion for Fourier hyperfunctions

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1997
Summary: A necessary and sufficient condition is proved that the asymptotic Taylor expansion for a Fourier hyperfunction converges in the space of Fourier hyperfunctions.
B Stanković
exaly   +2 more sources

Fourier Transformation of Power-Type Hyperfunctions

Mathematics and Its Application Japanese Series, 1992
In the preceding chapter, we explained the basic facts about the Fourier transformation of hyperfunctions and showed methods of calculating Fourier transforms of some simple hyperfunctions. In this chapter, we shall be concerned with Fourier transforms of the power-type hyperfunctions ∣x∣α (log ∣x∣)n H(x), ∣x∣α(log ∣x∣)n, ∣x∣α(log ∣x∣)n sgn x (α ...
Isao Imai, Imai Isao
exaly   +2 more sources