• Bulletin of the Korean Mathematical Society
• /
• v.17 no.2
• /
• pp.63-71
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• 1981

• Kyungpook Mathematical Journal
• /
• v.7 no.2
• /
• pp.47-55
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• 1967

• The Mathematical Education
• /
• v.16 no.1
• /
• pp.55-60
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• 1977

• Kyungpook Mathematical Journal
• /
• v.19 no.1
• /
• pp.9-21
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• 1979

• Kyungpook Mathematical Journal
• /
• v.5 no.2
• /
• pp.35-46
• /
• 1963

• Kyungpook Mathematical Journal
• /
• v.29 no.1
• /
• pp.57-63
• /
• 1989

• Kyungpook Mathematical Journal
• /
• v.8 no.2
• /
• pp.51-61
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• 1968

• Kyungpook Mathematical Journal
• /
• v.4 no.1
• /
• pp.5-12
• /
• 1961

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.3
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• pp.419-428
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• 2007

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 $\{T_\lambda\}$.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1785-1801
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• 2008

Noncommutative extensions of the Gross and Beltrami Laplacians, called the quantum Gross Laplacian and the quantum Beltrami Laplacian, resp., are introduced and their basic properties are studied. As noncommutative extensions of the Fourier-Gauss and Fourier-Mehler transforms, we introduce the quantum Fourier-Gauss and quantum Fourier- Mehler transforms. The infinitesimal generators of all differentiable one parameter groups induced by the quantum Fourier-Gauss transform are linear combinations of the quantum Gross Laplacian and quantum Beltrami Laplacian. A characterization of the quantum Fourier-Mehler transform is studied.