• Title/Summary/Keyword: Pseudodifferential operator

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SYMBOLS OF MINIMUM TYPE AND OF ZERO CLASS IN EXPONENTIAL CALCULUS

  • LEE, Chang Hoon
    • East Asian mathematical journal
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    • v.34 no.1
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    • pp.29-37
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    • 2018
  • We introduce formal symbols of product type, of zero class, and of minimum type and show that the formal power series representations for $e^p$ and $e^q$ are formal symbols of product type giving the same pseudodifferential operator, where p and q are formal symbols of minimum type and p - q is of zero class.

CONVOLUTORS FOR THE SPACE OF FOURIER HYPERFUNCTIONS

  • KIM KWANG WHOI
    • Journal of the Korean Mathematical Society
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    • v.42 no.3
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    • pp.599-619
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    • 2005
  • We define the convolutions of Fourier hyperfunctions and show that every strongly decreasing Fourier hyperfunction is a convolutor for the space of Fourier hyperfunctions and the converse is true. Also we show that there are no differential operator with constant coefficients which have a fundamental solution in the space of strongly decreasing Fourier hyperfunctions. Lastly we show that the space of multipliers for the space of Fourier hyperfunctions consists of analytic functions extended to any strip in $\mathbb{C}^n$ which are estimated with a special exponential function exp$(\mu|\chi|)$.

A NOTE ON SCATTERING OPERATOR SYMBOLS FOR ELLIPTIC WAVE PROPAGATION

  • Kim, Jeong-Hoon
    • Communications of the Korean Mathematical Society
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    • v.17 no.2
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    • pp.349-361
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    • 2002
  • The ill-posed elliptic wave propagation problems can be transformed into well-posed initial value problems of the reflection and transmission operators characterizing the material structure of the given model by the combination of wave field splitting and invariant imbedding methods. In general, the derived scattering operator equations are of first-order in range, nonlinear, nonlocal, and stiff and oscillatory with a subtle fixed and movable singularity structure. The phase space and path integral analysis reveals that construction and reconstruction algorithms depend crucially on a detailed symbol analysis of the scattering operators. Some information about the singularity structure of the scattering operator symbols is presented and analyzed in the transversely homogeneous limit.

THE SPACE OF FOURIER HYPERFUNCTIONS AS AN INDUCTIVE LIMIT OF HILBERT SPACES

  • Kim, Kwang-Whoi
    • Communications of the Korean Mathematical Society
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    • v.19 no.4
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    • pp.661-681
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    • 2004
  • We research properties of the space of measurable functions square integrable with weight exp$2\nu $\mid$x$\mid$$, and those of the space of Fourier hyperfunctions. Also we show that the several embedding theorems hold true, and that the Fourier-Lapace operator is an isomorphism of the space of strongly decreasing Fourier hyperfunctions onto the space of analytic functions extended to any strip in $C^n$ which are estimated with the aid of a special exponential function exp($\mu$|x|).