94 research outputs found
On spectral analysis of a magnetic Schrodinger operator on planar mixed automorphic forms
We characterize the space of the so-called planar mixed automorphic forms of
type with respect to an equivariant pair as the image
of the usual automorphic forms by an appropriate transform and we investigate
some concrete basic spectral properties of a magnetic Schrodinger operator
acting on them. The associated polynomials constitute classes of generalized
complex polynomials of Hermite type.Comment: 10 pages. This is a substantially reorganized, revised and improved
exposition. Misprints corrected and references added. Submitte
Generalized Binomial Probability Distributions attached to Landau levels on the Riemann sphere
A family of generalized binomial probability distributions attached to Landau
levels on the Riemann sphere is introduced by constructing a kind of
generalized coherent states. Their main statistical parameters are obtained
explicitly. As application, photon number statistics related to coherent states
under consideration are discussed.Comment: 12 pages, 1 figure. This is a revised and improved exposition. Typos
corrected and references adde
Singular -biharmonic problems involving the Hardy-Sobolev exponent
This paper is concerned with existence results for the singular
-biharmonic problem involving the Hardy potential and the critical
Hardy-Sobolev exponent. More precisely, by using variational methods combined
with the Mountain pass theorem and the Ekeland variational principle, we
establish the existence and multiplicity of solutions. To illustrate the
usefulness of our results, an illustrative example is also presented
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