RISS 검색 - 국내학술지논문

1
BOEHMIANS ON THE TORUS

Nemzer, Dennis Korean Mathematical Society 2006 대한수학회보 Vol.43 No.4
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By relaxing the requirements for a sequence of functions to be a delta sequence, a space of Boehmians on the torus ${\beta}(T^d)$ is constructed and studied. The space ${\beta}(T^d)$ contains the space of distributions as well as the space of hyperfunctions on the torus. The Fourier transform is a continuous mapping from ${\beta}(T^d)$ onto a subspace of Schwartz distributions. The range of the Fourier transform is characterized. A necessary and sufficient condition for a sequence of Boehmians to converge is that the corresponding sequence of Fourier transforms converges in $D'({\mathbb{R}}^d)$.
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Boehmians on the torus

Dennis Nemzer 대한수학회 2006 대한수학회보 Vol.43 No.4
- 원문보기
By relaxing the requirements for a sequence of func-tions to be a delta sequence, a space of Boehmians on the torus(Td) is constructed and studied. The space(Td) contains thespace of distributions as well as the space of hyperfunctions on thetorus. The Fourier transform is a continuous mapping from(Td)onto a subspace of Schwartz distributions. The range of the Fouriertransform is characterized. A necessary and sucient condition fora sequence of Boehmians to converge is that the corresponding se-quence of Fourier transforms converges inD0(Rd).
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ONE-PARAMETER GROUPS OF BOEHMIANS

Nemzer, Dennis Korean Mathematical Society 2007 대한수학회보 Vol.44 No.3
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The space of periodic Boehmians with $\Delta$-convergence is a complete topological algebra which is not locally convex. A family of Boehmians $\{T_\lambda\}$ such that $T_0$ is the identity and $T_{\lambda_1+\lambda_2}=T_\lambda_1*T_\lambda_2$ for all real numbers $\lambda_1$ and $\lambda_2$ is called a one-parameter group of Boehmians. We show that if $\{T_\lambda\}$ is strongly continuous at zero, then $\{T_\lambda\}$ has an exponential representation. We also obtain some results concerning the infinitesimal generator for $\{T_\lambda\}$.
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One-parameter groups of Boehmians

Dennis Nemzer 대한수학회 2007 대한수학회보 Vol.44 No.3
- 원문보기
The space of periodic Boehmians with {convergence is acomplete topological algebra which is not locally convex. A family ofBoehmians fT g such that T0 is the identity and T 1 + 2 = T 1 T 2 forall real numbers 1 and 2 is called a one-parameter group of Boehmians.We show that if fT g is strongly continuous at zero, thenfT g has anexponential representation. We also obtain some results concerning theinnitesimal generator for fT g.

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