Boundedness of Operators Related to a Degenerate Schrödinger Semigroup

2021 ◽  
Author(s):  
E. Harboure ◽  
O. Salinas ◽  
B. Viviani
Keyword(s):  
Schrödinger Semigroup

scholarly journals The Schrödinger Semigroup on Some Flat and Non Flat Manifolds

2013 ◽  
Vol 8 (2) ◽  
pp. 461-484 ◽  
Author(s):  
R. S. Kraußhar ◽  
M. M. Rodrigues ◽  
N. Vieira
Keyword(s):  
Schrödinger Semigroup ◽  
Flat Manifolds

On the images of Sobolev spaces under the Schrödinger semigroup

2019 ◽  
Vol 10 (1) ◽  
pp. 65-79 ◽  
Author(s):  
Sivaramakrishnan C ◽  
Sukumar D ◽  
Venku Naidu Dogga
Keyword(s):  
Sobolev Space ◽  
Bergman Space ◽  
Sobolev Spaces ◽  
Weighted Bergman Space ◽  
Hermite Operator ◽  
Schrödinger Semigroup ◽  
Similar Characterization

Abstract In this article, we consider the Schrödinger semigroup for the Laplacian Δ on {\mathbb{R}^{n}} , and characterize the image of a Sobolev space in {L^{2}(\mathbb{R}^{n},e^{u^{2}}du)} under this semigroup as weighted Bergman space (up to equivalence of norms). Also we have a similar characterization for Hermite Sobolev spaces under the Schrödinger semigroup associated to the Hermite operator H on {\mathbb{R}^{n}} .

scholarly journals The norm estimate of the difference between the Kac operator and the Schrödinger semigroup: A unified approach to the nonrelativistic and relativistic cases

1998 ◽  
Vol 149 ◽  
pp. 53-81 ◽  
Author(s):  
Takashi Ichinose ◽  
Satoshi Takanobu
Keyword(s):  
Schrödinger Operators ◽  
Product Formula ◽  
Operator Norm ◽  
Schrodinger Operators ◽  
Unified Approach ◽  
Trotter Product Formula ◽  
Nonrelativistic Case ◽  
Norm Estimate ◽  
Schrödinger Semigroup ◽  
The Difference

Abstract.An Lp operator norm estimate of the difference between the Kac operator and the Schrödinger semigroup is proved and used to give a variant of the Trotter product formula for Schrödinger operators in the Lp operator norm. The method of the proof is probabilistic based on the Feynman-Kac formula. The problem is discussed in the relativistic as well as nonrelativistic case.

scholarly journals Intrinsic ultracontractivity of a Schrödinger semigroup in RN

2009 ◽  
Vol 256 (12) ◽  
pp. 4095-4127 ◽  
Author(s):  
Bénédicte Alziary ◽  
Peter Takáč
Keyword(s):  
Intrinsic Ultracontractivity ◽  
Schrödinger Semigroup
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