Todor Gramchev

Classes of degenerate elliptic operators in Gelfand-Shilov spaces

We propose a novel approach for the study of the uniform regularity and the decay at infinity for Shubin type pseudo-differential operators which are globally hypoelliptic but not necessarily globally and even locally elliptic. The basic idea is to use the special role of the Hermite functions for the characterization of inductive and projective Gelfand-Shilov spaces. In this way we transform the problem to infinite dimensional linear systems on S Banach spaces of sequences by using Fourier series expansion with respect to the Hermite functions. As applications of our general results we obtain new theorems for global hypoellipticity for classes of degenerate operators in tensorized generalizations of Shubin spaces and in inductive and projective Gelfand-Shilov spaces.

Fractional derivative estimates in Gevrey spaces, global regularity and decay for solutions to semilinear equations in Rn

Abstract We propose a unified functional analytic approach to study the uniform analytic-Gevrey regularity and the decay of solutions to semilinear elliptic equations on R n . First, we develop a fractional calculus for nonlinear maps in Banach spaces of L p based Gevrey functions, 1 H p s ( R n ) regularity, with s>scr>0 depending on the nonlinearity. Next, we investigate the type of decay—polynomial or exponential—of the derivatives of solutions to semilinear elliptic equations, provided they decay a priori slowly as o(|x|−τ), |x|→∞ for some small τ>0. The restrictions, involved in our results, are optimal. In particular, given a hyperplane L, we construct 2d−2 strongly singular solutions (locally in H p s ( R n ) for s

PERTURBATIONS OF VECTOR FIELDS ON TORI: RESONANT NORMAL FORMS AND DIOPHANTINE PHENOMENA

This paper concerns perturbations of smooth vector fields on

Rapidly convergent iteration method for simultaneous normal forms of commuting maps

\mathbb{T}^n

Compact solitary waves in linearly elastic chains with non-smooth on-site potential

(constant if

Sub-exponential decay and uniform holomorphic extensions for semilinear pseudodifferential equations

n\geq3

Gelfand-Shilov spaces, pseudo-differential operators and localization operators

) with zeroth-order

Exponential Decay and Regularity for SG-elliptic Operators with Polynomial Coefficients

C^\infty

First order pseudodifferential operators on the torus: Normal forms, diophantine phenomena and global hypoellipticity

and Gevrey

Global Regularity and Stability in S-Spaces for Classes of Degenerate Shubin Operators

G^\sigma