논문KCI 등재
Regularity of the Schr\"odinger Equation for a Cauchy-Euler Type Operator
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We consider the initial value problem of the Schr\"odinger equation for an interesting Cauchy-Euler type operator $\mathscr R$ on $\C^n$ that is an analogue of the harmonic oscillator in $\R^n$. We get an appropriate $L^{1} - L^{\infty}$ dispersive estimate for the solution of the initial value problem.
Abstract
We consider the initial value problem of the Schr\"odinger equation for an interesting Cauchy-Euler type operator $\mathscr R$ on $\C^n$ that is an analogue of the harmonic oscillator in $\R^n$. We get an appropriate $L^{1} - L^{\infty}$ dispersive estimate for the solution of the initial value problem.
참고문헌 (7)
- V. Bargmann, "On a Hilbert space of analytic functions and an associated integral transform I", Comm. Pure Appl. Math, 14, pp.187~214 (1961)
- H. R. Cho, "Boundedness of the Segal-Bargmann Transform on Fractional Hermite-Sobolev Spaces", Journal of Function Spaces, 2017, pp.6~ (2017)
- K.-J. Engel, "One-Parameter Semigroups for Linear Evolution Equations" (2000), Springer-Verlag
- R. P. Feynman, "Quantum mechanics and path integrals" (1965), McGraw-Hill
- A. K. Nandakumaran, "Schr¨odinger equation and the oscillatory semigroup for the Hermite operator", J. Funct. Anal, 224, pp.371~385 (2005)
- E. Stein, "Interpolation of operators with change of measures", Trans. Amer. Math. Soc, 87, pp.159~172 (1958)
- K. Zhu, "Analysis on Fock spaces" (2012), Springer
관련 논문AI추천
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