This paper discusses some spectral properties of class wF(p,r,q) operators for p > 0, r > 0, p + r ≤ 1, and q ≥ 1. It is shown that if T is a class wF(p,r,q) operator, then the Riesz idempotent Eλ of T with respect to each nonzero isolated point spectrum λ is selfadjoint and Eλ = ker(T − λ)= ker(T − λ)∗ . Afterwards, we prove that every class wF(p,r,q) operator has SVEP and property (β), andWey...

The authors consider the multilinear Riesz potential operator defined by Iα,m − → f x ∫ Rd m f1 y1 f2 y2 · · · fm ym /| x−y1, . . . , x−ym |mn−α dμ y1 · · ·dμ ym , where − → f denotes themtuple f1, f2, . . . , fm , m,n the nonnegative integers with n ≥ 2, m ≥ 1, 0 < α < mn, and μ is a nonnegative n-dimensional Borel measure. In this paper, the boundedness for the operator Iα,m on the product of...

We consider the (projective) representations of the group of holomorphic automorphisms of a symmetric tube domain V ⊕ iΩ that are obtained by analytic continuation of the holomorphic discrete series. For a representation corresponding to a discrete point in the Wallach set, we find the decomposition under restriction to the identity component of GL(Ω). Using Riesz distributions, an explicit int...

Context and objectives In image processing, the Riesz transform was introduced as a possible extension of the Hilbert Transform in general dimension: it has many applications, like the extraction of local features in 2D signals, the demodulation of holograms, or the analysis of color images. The most easy way to implement the Riesz transform is to compute its Fourier representation by mean of 2...

Given a complex Banach space X, we investigate the stable character of property (VE) for bounded linear operator T:X→X, under commuting perturbations that are Riesz, compact, algebraic and hereditarily polaroid. We also analyze sufficient conditions allow transfer from tensorial factors T S to its tensor product.

The generalized Bochner-Riesz operator SR,λ may be defined as Sf(x) = F−1 [( 1− ρ R )λ + f̂ ] (x) where ρ is an appropriate distance function and F−1 is the inverse Fourier transform. The sharp bound ‖Sf‖L4(R2×R2) ≤ C‖f‖L4(R2×R2) is shown for the distance function ρ(ξ′, ξ”) = max{|ξ′|, |ξ′′|}. This is a rough distance function corresponding to the R4 cylinder analog {(x1, x2, x3, x4) ∈ R4, x1+ x...

We study the optimal approximation of the solution of an operator equation A(u) = f by linear mappings of rank n and compare this with the best n-term approximation with respect to an optimal Riesz basis. We consider worst case errors, where f is an element of the unit ball of a Hilbert space. We apply our results to boundary value problems for elliptic PDEs that are given by an isomorphism A :...

In this work we will investigate how to find a matrix representation of operators on a Hilbert space H with Bessel sequences, frames and Riesz bases as an extension of the known method of matrix representation by ONBs. We will give basic definitions of the functions connecting infinite matrices defining bounded operators on l and operators onH. We will show some structural results and give some...

In this paper, we give some properties of the left and right finite Caputo derivatives. Such derivatives lead to finite Riesz type fractional derivative, which could be considered as the fractional power of the Laplacian operator modelling the dynamics of many anomalous phenomena in super-diffusive processes. Finally, the exact solutions of certain fractional diffusion partial differential equa...

We consider the generalized Schrr odinger operator ? + where is a nonnegative Radon measure in R n , n 3. Assuming that satisses certain scale-invariant Kato condition and doubling condition, we establish the following bounds for the fundamental solution of ? + in R n : where d(x; y;) is the distance function for the modiied Agmon metric m(x;)dx 2 associated with. We also study the boundedness ...