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THE SCHR\"ODINGER EQUATION FOR AN EULER OPERATOR ON FOCK SPACES

Hong Rae Cho
영남수학회 (Youngnam Mathematical Society)|2024.09|East Asian Mathematical Journal|제40권 제5호|pp. 515-526

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참고문헌

키워드

Euler operatorFock spaceSchr¨odinger equationHermite oper- atorBargmann transformEuler semigroup.
주제분류수학

초록

We consider the initial value problem of the Schr\"odinger equation for an Euler operator $\mathcal R$ on $\C^n$ that is an analogue of the harmonic oscillator in $\R^n$. We get some regularity results of the Schr\"odinger equation on Fock spaces.

Abstract

We consider the initial value problem of the Schr\"odinger equation for an Euler operator $\mathcal R$ on $\C^n$ that is an analogue of the harmonic oscillator in $\R^n$. We get some regularity results of the Schr\"odinger equation on Fock spaces.

참고문헌 (9)

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  3. K. -J. Engel, "One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics 194" (2000), Springer-Verlag
  4. R. P. Feynman, "Quantum mechanics and path integrals" (1965), McGraw-Hill
  5. L. Gross, "Logarithmic Sobolev inequalities", Amer. J. Math, 97, pp.1061~1083 (1975)
  6. A. K. Nandakumaran, "Schr¨odinger equation and the oscillatory semigroup for the Hermite operator", J. Funct. Anal, 224, pp.371~385 (2005)
  7. E. Stein, "Interpolation of operators with change of measures", Trans. Amer. Math. Soc, 87, pp.159~172 (1958)
  8. P. R. Stinga, "Regularity theory for the fractional harmonic oscillator", J. Funct. Anal, 260(10), pp.3097~3131 (2011)
  9. K. Zhu, "Analysis on Fock spaces, Graduate Texts in Mathematics, 263" (2012), Springer

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