[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.7858/eamj.2019.001

REGULARITY OF THE SCHRÖDINGER EQUATION FOR A CAUCHY-EULER TYPE OPERATOR

CHO, HONG RAE (DEPARTMENT OF MATHEMATICS, PUSAN NATIONAL UNIVERSITY)
LEE, HAN-WOOL (DEPARTMENT OF MATHEMATICS, PUSAN NATIONAL UNIVERSITY)
CHO, EUNSUNG (DEPARTMENT OF MATHEMATICS, PUSAN NATIONAL UNIVERSITY)

Publication Information

East Asian mathematical journal / v.35, no.1, 2019 , pp. 1-7 More about this Journal

Abstract

We consider the initial value problem of the Schrodinger equation for an interesting Cauchy-Euler type operator ${\mathfrak{R}}$ on ${\mathbb{C}}^n$ that is an analogue of the harmonic oscillator in ${\mathbb{R}}^n$ . We get an appropriate $L^1-L^{\infty}$ dispersive estimate for the solution of the initial value problem.

Keywords

Fock space; Schrodinger equation; Cauchy-Euler type operator; Oscillatory semigroup;

Citations & Related Records

Reference

1	V. Bargmann, On a Hilbert space of analytic functions and an associated integral transform I, Comm. Pure Appl. Math. 14 (1961), 187-214. DOI
2	H. R. Cho, H. Choi, and H.-W. Lee, Boundedness of the Segal-Bargmann Transform on Fractional Hermite-Sobolev Spaces, Journal of Function Spaces, Volume 2017 (2017), Article ID 9176914, 6 pages.
3	K.-J. Engel and R. Nagel. One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics 194, Springer-Verlag, Berlin, New York, 2000.
4	R. P. Feynman and A. R. Hibbs, Quantum mechanics and path integrals, McGraw-Hill, Maidenhead, 1965.
5	A. K. Nandakumaran and P. K. Ratnakumar, Schrodinger equation and the oscillatory semigroup for the Hermite operator, J. Funct. Anal. 224 (2005), 371-385. DOI
6	E. Stein and G. Weiss, Interpolation of operators with change of measures, Trans. Amer. Math. Soc. 87 (1958), 159-172. DOI
7	K. Zhu, Analysis on Fock spaces, Graduate Texts in Mathematics, 263. Springer, New York, 2012.