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SUMMARY:Intertwining operators beyond the stark effect
DTSTART:20260619T131500Z
DTEND:20260619T140500Z
DTSTAMP:20260615T222500Z
UID:indico-event-1406@math-events.uni-bonn.de
DESCRIPTION:Speakers: Ying Wang (Basque Center for Applied Mathematics)\n\
 nAbstract:\nThe main mathematical manifestation of the Stark effect in qua
 ntum mechanics is the shift and the formation of clusters of eigenvalues w
 hen a spherical Hamiltonian is perturbed by lower order terms. Understandi
 ng this mechanism turned out to be fundamental in the description of the l
 arge-time asymptotics of the associated Schrödinger groups and can be res
 ponsible for the lack of dispersion [1\, 2\, 3]. Recently\, Miao\, Su\, an
 d Zheng introduced in [4] a family of spectrally projected intertwining op
 erators\, reminiscent of the Kato’s wave operators\, in the case of cons
 tant perturbations on the sphere (inverse-square potential)\, and also pro
 ved their boundedness in $L^p$. Our aim is to establish a general framewor
 k in which some suitable intertwining operators can be defined also for no
 n constant spherical perturbations in space dimensions 2 and higher\, furt
 hermore we investigate the mapping properties between $L^p$-spaces of thes
 e operators. In 2D\, we prove a complete result\, for the Schrödinger Ham
 iltonian with a (fixed) magnetic potential an electric potential\, both sc
 aling critical. In higher dimensions\, apart from recovering the example o
 f inverse-square potential\, we can conjecture a complete result in presen
 ce of some symmetries (zonal potentials)\, and open some interesting spect
 ral problems concerning the asymptotics of eigenfunctions. This is a joint
 ed work with Luca Fanelli\, Xiaoyan Su\, Junyong Zhang and Jiqiang Zheng.\
 n[1] T. Kato\, Perturbation theory for linear operators\, Springer-Verlag\
 , Berlin\, 1966.\n[2] C. E. Kenig\, A. Ruiz\, and C. D. Sogge\, Uniform So
 bolev inequalities and unique continuation for second order constant coeff
 icient differential operators\, Duke Math. J.\, 55 (1987)\, 329-347.\n[3] 
 B. G. Korenev\, Bessel Functions and Their Applications\, An International
  Series of Monographs in Mathematics\, Taylor and Francis\, 11 New Fetter 
 Lane\, London EC4P 4EE\, 2002.\n[4] G. N. Watson\, A Treatise on the Theor
 y of Bessel Functions. Second Edition\, Cambridge University Press\, 1944.
  \n \n\nhttps://math-events.uni-bonn.de/event/1406/
LOCATION:Endenicher Allee 60\, Seminarraum 0.011 (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/1406/
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