The associated evolution operators which map u(0, ·) to u(t, ·) is the family of Fourier multipliers e, e := F e F . (2) Our main result shows that boundedness in L for p 6= 2 is very rare. The evolution operator is L bounded if and only if it consists of simple translations. If the multiplier (2) is an L multiplier then it is an L multiplier for the dual index, p+q = 1. By interpolation it is ...

for a ∈ mn, the schur multiplier of a is defined as s a(x) =a ◦ x for all x ∈ mn and the spectral norm of s a can be stateas ∥s a∥ = supx,0 ∥a ∥x ◦x ∥ ∥. the other norm on s a can be definedas ∥s a∥ω = supx,0 ω(ω s( ax (x ) )) = supx,0 ωω (a (x ◦x ) ), where ω(a) standsfor the numerical radius of a. in this paper, we focus on therelation between the norm of schur multiplier of product of matric...

The theory of  continuous frames in Hilbert spaces is extended, by using the concepts of measure spaces, in order to get the results of a new application of operator theory.  The $K$-frames were  introduced by G$breve{mbox{a}}$vruta (2012) for Hilbert spaces to study atomic systems with respect to a bounded linear operator. Due to the structure of  $K$-frames, there are many differences between...

This note describes the pleasant features that accrue in weighted settings when the partial sums of the operator-valued Fourier series corresponding to a multiplier function ψ : T → C are uniformly bounded in operator norm. This circle of ideas also includes a Tauberiantype condition on the multiplier function ψ sufficient to insure such uniform boundedness of partial sums. These considerations...

We introduce the notion of a C *-valued weight between two C *-algebras as a generalization of an ordinary weight on a C *-algebra and as a C *-version of operator valued weights on von Neumann algebras. Also, some form of lower semi-continuity will be discussed together with an extension to the Multiplier algebra. A strong but useful condition for C *-valued weights, the so-called regularity, ...

Frame theory has a great revolution for recent years. This been extended from Hilbert spaces to C ∗ -modules. In this paper, we define and study the new concept of controlled continuous id="M6"> - id="M7"> K id="M8"> g -frames id="M9"> -modules establish some prope...

We consider a circular arch of thickness ε and curvature r−1 whose elastic deformations are described by a 2×2 system of linear partial differential equation. The system of the type y′′ + Ay = 0,y = (y1, y3) involves the tangential y1 and normal y3 component of the arch displacement. We analyze in this work the null controllability of these two components by acting on the boundary through a Dir...

Abstract Let $$\Gamma &lt; G$$ Γ &lt; G be a discrete subgroup of locally compact unimodular group G . $$m\in C_b(G)$$ m ∈ C b ( )</mml:m...