When does the norm of a Fourier multiplier dominate its L∞ norm?

Schur multiplier norm of product of matrices

For A ∈ <span style="font-family...

The Norm of the L'-fourier Transform on Unimodular Groups

We discuss sharpness in the Hausdorff Young theorem for unimodular groups. First the functions on unimodular locally compact groups for which equality holds in the Hausdorff Young theorem are determined. Then it is shown that the Hausdorff Young theorem is not sharp on any unimodular group which contains the real Une as a direct summand, or any unimodular group which contains an Abelian normal ...

schur multiplier norm of product of matrices

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...

Resolvent Norm Decay Does Not Characterize Norm Continuity

It is the fundamental principle of semigroup theory that the behavior of a strongly continuous semigroup (T (t))t≥0 on a Banach space X and the properties of its generator (A,D(A)), or equivalently the properties of the resolvent function R(λ,A) = (λ − A)−1 (λ ∈ C), should closely correlate. Indeed, the Laplace transform carries the regularity properties of the semigroup to the resolvent functi...

The Norm Game - How a Norm Fails