In this paper we apply a method of spectral theory of linear operators [10] to establish relations between the support of a function f on R with properties of its image Tf under a linear operator T : R → R. The classical approach uses analytic continuation of the image Tf into some complex domain (theorems of Paley-Wiener type [4, 5, 6, 7]), and therefore, could not apply to functions whose ima...

Let Ck = ( 2k k ) /(k+1) denote the k-th Catalan number and put ak(x) = Ck+Ck−1x+· · ·+C0x . Define the (n+1)×(n+1) Hankel determinant by setting Hn(x) = det[ai+j(x)]0≤i,j≤n. Even though Hn(x) does not admit a product form evaluation for arbitrary x, the recently introduced technique of γ-operators is applicable. We illustrate this technique by evaluating this Hankel determinant as Hn(x) = n ∑

Let m have compact support in (0,∞). For 1 < p < 2d/(d + 1), we give a necessary and sufficient condition for the Lprad(R )-boundedness of the maximal operator associated with the radial multiplier m(|ξ|). More generally we prove a similar result for maximal operators associated with multipliers of modified Hankel transforms. The result is obtained by modifying the proof of the characterization...

In a recent paper we have presented a method to evaluate certain Hankel determinants as almost products; i.e. as a sum of a small number of products. The technique to find the explicit form of the almost product relies on differential-convolution equations and trace calculations. In the trace calculations a number of intermediate nonlinear terms involving determinants occur, but only to cancel ...

In this paper, we consider weighted composition operators betweenmeasurable differential forms and then some classic properties of these operators are characterized.

We consider the problem of approximating functions by sums of wave packets. Our objective is to find sparse decompositions of image functions, over a finite range of scales. We also address the naturally connected task of approximating the wavefront set, computationally. We formulate the problem in terms of Hankel operators, Hankel matrices and their low-rank approximations, and develop an alge...

in this article, we discuss measure theoretic characterizations for weighted composition operators in some operator classes on $l^{2}(sigma)$ such as, $n$-power normal, $n$-power quasi-normal, $k$-quasi-paranormal and quasi-class$a$. then we show that weighted composition operators can separate these classes.

Hankel operators on the Hardy space of the disk, H (D) , can be studied as linear operators from H (D) to its dual space, as conjugate linear operators from H (D) to itself, or, in the viewpoint we will take here, as bilinear functionals on H (D) × H (D) . In that formulation, given a holomorphic symbol function b we consider the bilinear Hankel form, defined initially for f, g in P (D) , the s...