On the images of Sobolev spaces under the Schrödinger semigroup
-
Sivaramakrishnan C
Abstract
In this article, we consider the Schrödinger semigroup for the Laplacian Δ on
Funding statement: The first author thanks University Grant Commission, India, for financial support.
Acknowledgements
The authors wish to thank G. B. Folland for giving clarification to their questions related to weighted Sobolev spaces.
References
[1] V. Bargmann, On a Hilbert space of analytic functions and an associated integral transform, Comm. Pure Appl. Math. 14 (1961), 187–214. 10.1002/cpa.3160140303Suche in Google Scholar
[2] D.-W. Byun, Inversions of Hermite semigroup, Proc. Amer. Math. Soc. 118 (1993), no. 2, 437–445. 10.1090/S0002-9939-1993-1145414-6Suche in Google Scholar
[3] G. B. Folland, Harmonic Analysis in Phase Space, Ann. of Math. Stud. 122, Princeton University Press, Princeton, 1989. 10.1515/9781400882427Suche in Google Scholar
[4] B. C. Hall, The inverse Segal–Bargmann transform for compact Lie groups, J. Funct. Anal. 143 (1997), no. 1, 98–116. 10.1006/jfan.1996.2954Suche in Google Scholar
[5] B. C. Hall and W. Lewkeeratiyutkul, Holomorphic Sobolev spaces and the generalized Segal–Bargmann transform, J. Funct. Anal. 217 (2004), no. 1, 192–220. 10.1016/j.jfa.2004.03.018Suche in Google Scholar
[6] N. Hayashi and S. Saitoh, Analyticity and smoothing effect for the Schrödinger equation, Ann. Inst. H. Poincaré Phys. Théor. 52 (1990), no. 2, 163–173. Suche in Google Scholar
[7] B. Krötz, G. Ólafsson and R. J. Stanton, The image of the heat kernel transform on Riemannian symmetric spaces of the noncompact type, Int. Math. Res. Not. IMRN (2005), no. 22, 1307–1329. 10.1155/IMRN.2005.1307Suche in Google Scholar
[8] B. Krötz, S. Thangavelu and Y. Xu, The heat kernel transform for the Heisenberg group, J. Funct. Anal. 225 (2005), no. 2, 301–336. 10.1016/j.jfa.2005.03.019Suche in Google Scholar
[9] S. Parui, P. K. Ratnakumar and S. Thangavelu, Analyticity of the Schrödinger propagator on the Heisenberg group, Monatsh. Math. 168 (2012), no. 2, 279–303. 10.1007/s00605-012-0424-7Suche in Google Scholar
[10] R. Radha and S. Thangavelu, Holomorphic Sobolev spaces, Hermite and special Hermite semigroups and a Paley–Wiener theorem for the windowed Fourier transform, J. Math. Anal. Appl. 354 (2009), no. 2, 564–574. 10.1016/j.jmaa.2009.01.021Suche in Google Scholar
[11] R. Radha, S. Thangavelu and D. Venku Naidu, On the images of Sobolev spaces under the heat kernel transform on the Heisenberg group, Math. Nachr. 286 (2013), no. 13, 1337–1352. 10.1002/mana.201100233Suche in Google Scholar
[12] S. Thangavelu, An Introduction to the Uncertainty Principle, Progr. Math. 217, Birkhäuser, Boston, 2004. 10.1007/978-0-8176-8164-7Suche in Google Scholar
© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Convolution operators on measure algebras of KPC-hypergroups
- Infinitely many solutions for a class of fourth-order impulsive differential equations
-
Existence of positive solutions for nonlocal
- Commutative and non-commutative bialgebras of quasi-posets and applications to Ehrhart polynomials
- On the images of Sobolev spaces under the Schrödinger semigroup
Artikel in diesem Heft
- Frontmatter
- Convolution operators on measure algebras of KPC-hypergroups
- Infinitely many solutions for a class of fourth-order impulsive differential equations
-
Existence of positive solutions for nonlocal
- Commutative and non-commutative bialgebras of quasi-posets and applications to Ehrhart polynomials
- On the images of Sobolev spaces under the Schrödinger semigroup
