Let Sp(n,R) be the symplectic group, and K∗ n its maximal compact subgroup. Then G = Sp(n,R)/K∗ n can be realized as the Siegel domain of type one. The square-integrable representation of G gives the admissible wavelets AW and wavelet transform. The characterization of admissibility condition in terms of the Fourier transform is given. The Bergman kernel follows from the viewpoint of coherent s...

We generate solvable cases of the two angular equations resulting from variable separation in three-dimensional Dunkl-Schrödinger equation expressed spherical coordinates. It is shown that Dunkl formalism interrelates these with trigonometric Pöschl-Teller systems. Based on this interrelation, we use point transformations and Darboux-Crum to construct new equations. Instead stationary energy, c...

Certain objects of conformal field theory, for example partition functions on the rectangle and torus, one-point are either invariant or transform simply under modular group, properties which should be preserved $T\overline T$ deformation. The formulation proof this statement in fact extents to more general such as deformed Jacobi forms. We show that deformation acts their Mellin transform, mul...

Abstract. We introduce a spectral transform for the finite relativistice Toda lattice (RTL) in generalized form. In the nonrelativistic case, Moser constructed a spectral transform from the spectral theory of symmetric Jacobi matrices. Here we use a nonsymmetric generalized eigenvalue problem for a pair of bidiagonal matrices (L, M) to define the spectral transform for the RTL. The inverse spec...

We devise a framework encompassing the classical theory of characteristics and the theory valid in the convex case recently obtained by R.T. Rockafellar and P. Wolenski. It relies on a notion of transform introduced by I. Ekeland. It involves a class of functions called Ekeland functions which is large enough to encompass convex functions, concave functions and linear-quadratic functions, as we...

In the framework of toroidal Pseudodifferential operators on the flat torus Tn := (R/2πZ)n we begin by proving the closure under composition for the class of Weyl operators Opw ~ (b) with simbols b ∈ Sm(Tn × Rn). Subsequently, we consider Opw ~ (H) when H = 1 2 |η| + V (x) where V ∈ C(T;R) and we exhibit the toroidal version of the equation for the Wigner transform of the solution of the Schröd...

It is important to seek for more explicit exact solutions of nonlinear partial differential equations (NLPDEs) in mathematical physics. With the help of symbolic computation software like Maple or Mathematica, much work has been focused on the various extensions and applications of the known methods to construct exact solutions of NLPDEs. Mathematical modelling of physical systems often leads t...

Following Shastry and Sutherland I construct the super Lax operators for the Calogero model in the oscillator potential. These operators can be used for the derivation of the eigenfunctions and integrals of motion of the Calogero model and its supersymmetric version. They allow to infer several relations involving the Lax matrices for this model in a fast way. It is shown that the super Lax ope...