This paper is concerned with nonautonomous differential equations in Banach spaces. Using the theory of semigroups of linear and nonlinear operators one investigates the semigroups of weighted translation operators associated with the underlying equations. Necessary and sufficient conditions for different types of stability are given in terms of spectral properties of the translation operators ...

Approaches to approximate diagonalization of variable-coefficient differential operators using similarity transformations are presented. These diagonalization techniques are inspired by the interpretation of the Uncertainty Principle by Fefferman, known as the SAK Principle, that suggests the location of eigenfunctions of self-adjoint differential operators in phase space. The similarity transf...

This paper contains proofs of most of the results announced in [9], together with some further developments. The basic analytic question addressed here concerns the mapping properties, on the natural Sobolev spaces, of elliptically totally characteristic pseudodifferential operators, on a compact C∞ manifold with boundary. The ring, Ψb (X), of such operators was described in detail in [8] and i...

In this article, the recurrence relations and shift operators for multivariate Hermite polynomials are derived using factorization approach. Families of differential equations, including differential, integro–differential, partial obtained these operators. The Volterra integral is also discovered.