Abstract Originating with the famous monograph by Dan Henry, semigroup approach to evolution problems having a positive sectorial operator in main part allows us settle them at various levels of fractional power scale associated linear operator. This translates into different regularity properties local solutions such equations. Specific applications abstract results 2D surface quasi-geostrophi...

A sectorial matrix is an n×n whose numerical range contained in open half-plane, and such matrices have many nice properties. In particular, the subset of strictly accretive a convex cone space matrices, results related to positive definite recently been generalized this cone. Moreover, used define phases matrix, these can be angularly bound eigenvalues by majorization-type inequalities similar...

In this paper we consider optimal control problems in which a certain L1-type norm of the control appears in the objective. Problems of this type are of interest for at least two reasons. Firstly, the L1 norm of the control is often a natural measure of the control cost. Secondly, this term promotes sparsely supported optimal controls, i.e., controls which are zero on substantial parts of its d...

We prove Paley-Littlewood decompositions for the scales of fractional powers of 0-sectorial operators A on a Banach space which correspond to Triebel-Lizorkin spaces and the scale of Besov spaces if A is the classical Laplace operator on L(R). We use the H∞calculus, spectral multiplier theorems and generalized square functions on Banach spaces and apply our results to Laplace-type operators on ...