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Properties of the Sobolev space H k s , s '

Henryk Kołakowski (1999)

Annales Polonici Mathematici

Let n ≥ 2 and H k s , s ' = u S ' ( n ) : u s , s ' < , where u ² s , s ' = ( 2 π ) - n ( 1 + | ξ | ² ) s ( 1 + | ξ ' | ² ) s ' | F u ( ξ ) | ² d ξ , F u ( ξ ) = e - i x ξ u ( x ) d x , ξ ' k , k < n. We prove that for some s,s’ the space H k s , s ' is a multiplicative algebra.

Properties of two variables Toeplitz type operators

Elżbieta Król-Klimkowska, Marek Ptak (2016)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

The investigation of properties of generalized Toeplitz operators with respect to the pairs of doubly commuting contractions (the abstract analogue of classical two variable Toeplitz operators) is proceeded. We especially concentrate on the condition of existence such a non-zero operator. There are also presented conditions of analyticity of such an operator.

Proximal normal structure and relatively nonexpansive mappings

A. Anthony Eldred, W. A. Kirk, P. Veeramani (2005)

Studia Mathematica

The notion of proximal normal structure is introduced and used to study mappings that are "relatively nonexpansive" in the sense that they are defined on the union of two subsets A and B of a Banach space X and satisfy ∥ Tx-Ty∥ ≤ ∥ x-y∥ for all x ∈ A, y ∈ B. It is shown that if A and B are weakly compact and convex, and if the pair (A,B) has proximal normal structure, then a relatively nonexpansive mapping T: A ∪ B → A ∪ B satisfying (i) T(A) ⊆ B and T(B) ⊆ A, has a proximal point in the sense that...

Pseudo almost periodic and automorphic mild solutions to nonautonomous neutral partial evolution equations

Abdelkarim-Nidal Akdad, Khalil Ezzinbi, Lotti Souden (2015)

Nonautonomous Dynamical Systems

In this work, we present a new concept of Stepanov weighted pseudo almost periodic and automorphic functions which is more generale than the classical one, and we obtain a new existence result of μ-pseudo almost periodic and μ-pseudo almost automorphic mild solutions for some nonautonomous evolution equations with Stepanov μ-pseudo almost periodic terms. An example is shown to illustrate our results.

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