Schrödinger equation and the oscillatory semigroup for the Hermite operator |
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| Authors: | AK Nandakumaran PK Ratnakumar |
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| Institution: | a Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India
b School of Mathematics, Harish Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India |
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| Abstract: | We discuss the regularity of the oscillatory semigroup eitH, where H=-Δ+|x|2 is the n-dimensional Hermite operator. The main result is a Strichartz-type estimate for the oscillatory semigroup eitH in terms of the mixed Lp spaces. The result can be interpreted as the regularity of solution to the Schrödinger equation with potential V(x)=|x|2. |
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| Keywords: | primary 33C45 secondary 35G10 35J10 |
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