A note on the wave packet transforms

A note on the comparison between Laplace and Sumudu transforms

A note on $lambda$-Aluthge transforms of operators

Let $A=U|A|$ be the polar decomposition of an operator $A$ on a Hilbert space $mathscr{H}$ and $lambdain(0,1)$. The $lambda$-Aluthge transform of $A$ is defined by $tilde{A}_lambda:=|A|^lambda U|A|^{1-lambda}$. In this paper we show that emph{i}) when $mathscr{N}(|A|)=0$, $A$ is self-adjoint if and only if so is $tilde{A}_lambda$ for some $lambdaneq{1over2}$. Also $A$ is self adjoint if and onl...

a note on the comparison between laplace and sumudu transforms

A Note on Dichotomies for Metric Transforms

We show that for every nondecreasing concave function ω : [0,∞) → [0,∞) with ω(0) = 0, either every finite metric space embeds with distortion arbitrarily close to 1 into a metric space of the form (X,ω◦d) for some metric d on X, or there exists α = α(ω) > 0 and n0 = n0(ω) ∈ N such that for all n > n0, any embedding of {0, . . . , n} ⊆ R into a metric space of the form (X,ω ◦ d) incurs distorti...

On the fractional Fourier and continuous fractional wave packet transforms of almost periodic functions

We state the fractional Fourier transform and the continuous fractional wave packet transform as ways for analyzing persistent signals such as almost periodic functions and strong limit power signals. We construct frame decompositions for almost periodic functions using these two transforms. Also a norm equality of this signal is given using the continuous fractional wave packet transform.