Related papers: An explicit formula for the cubic Szeg\"o equation

We obtain Szeg\H o-type limit theorems for Toeplitz operators on the weighted Bergman spaces $A^{2}_{\alpha}(\mathbb{B}^{n})$, and on $L^{2}(G)$, presenting separate formulations for compact and locally compact Abelian groups. Furthermore,…

In this paper, we exploit the concavity of sums of Hessian operators to derive Pogorelov estimates for corresponding equations under the dynamic semi-convexity assumption, and we further obtain several Liouville-type results. Moreover, when…

In the framework of infinite ergodic theory, we derive equidistribution results for suitable weighted sequences of cusp points of Hecke triangle groups encoded by group elements of constant word length with respect to a set of natural…

We present explicit formulas for Hecke eigenforms as linear combinations of q-analogues of modified double zeta values. As an application, we obtain period polynomial relations and sum formulas for these modified double zeta values. These…

In this paper we consider a class of fully nonlinear forced and reversible Schroedinger equations and prove existence and stability of quasi-periodic solutions. We use a Nash-Moser algorithm together with a reducibility theorem on the…

We show how to construct a non-smooth solution to Hessian fully nonlinear second-order uniformly elliptic equation using the Cartan isoparametric cubic in 5 dimensions.

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The number of periodic solutions to Painlev\'e VI along a Pochhammer loop is counted exactly. It is shown that the number grows exponentially with period, where the growth rate is determined explicitly. Principal ingredients of the…

Quasi-periodic solutions of the KP hierarchy acted by vertex operators are studied. We show, with the aid of the Sato Grassmannian, that solutions thus constructed correspond to torsion free rank one sheaves on some singular algebraic…

Estimation of linear and quadratic functionals over different classes of univalent functions is one of the classical problems in geometric function theory. In this paper we solve the problem over some classes of so-called non-linear…

In evolution equations for a complex amplitude, the phase obeys a much more intricate equation than the amplitude. Nevertheless, general methods should be applicable to both variables. On the example of the traveling wave reduction of the…

We consider the Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are rational functions generated by elements of the symmetric group $S_{n}$. We assume that parameter $\rho=\pm{1}$. In previous…

I prove that quasi-periodic Schr\"odinger operators in arbitrary dimension have some absolutely continuous spectrum.

We obtain explicit expressions for genus 2 degenerate sigma-function in terms of genus $1$ sigma-function and elementary functions as solutions of a system of linear PDEs satisfied by the sigma-function. By way of application we derive a…

We shall deal with the periodic problem for nonlinear perturbations of abstract hyperbolic evolution equations generating an evolution system of contractions. We prove an averaging principle for the translation along trajectories operator…

We define graded hyper-algebras of vector-valued Siegel modular forms, which allow us to study tensor products of the latter. We also define vector-valued Hecke operators for Siegel modular forms at all places of ${\mathbb Q}$, acting on…

We prove that a Hamilton-Jacobi equation in 1D with periodic forcing has a set of generalized solutions such that each solution is a sum of linear and continuous periodic functions; we also give a condition of uniqueness of this solution in…

We generalize some classical results for the Schlesinger system of partial differential equations and give the explicit form of its solution, associated with rational matrix functions in general position.

Hecke algebras are beautiful q-extensions of Coxeter groups. In this paper, we prove several results on their characters, with an emphasis on characters induced from trivial and sign representations of parabolic subalgebras. While most of…

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