In this paper we establish a mean value property for the functions which is satisfied to Laplace–Bessel equation. Our results involve generalized divergence theorem and second Green’s identities relating bulk with boundary of region on differential Bessel operators act. Also design fractional weighted operator, study its boundedness, obtain maximal inequality spherical get boundedness. The conn...

Recent work on Euclidean quantum gravity on the four-ball has proved regularity at the origin of the generalized zeta-function built from eigenvalues for metric and ghost modes, when diffeomorphism-invariant boundary conditions are imposed in the de Donder gauge. The hardest part of the analysis involves one of the four sectors for scalar-type perturbations, the eigenvalues of which are obtaine...

Quasi-invariance under translation is established for the σ-finite measure unifying Brownian penalisations, which has been introduced by Najnudel, Roynette and Yor ([10]). For this purpose, the theory of Wiener integrals for centered Bessel processes, due to Funaki, Hariya and Yor ([5]), plays a key role.

Generalized fusion frame and some of their properties in tensor product Hilbert spaces are described. Also, the canonical dual g-fusion is considered. Finally, operator for a pair Bessel sequences presented.

the theory of c-frames and c-bessel mappings are the generalizationsof the theory of frames and bessel sequences. in this paper, weobtain several equivalent conditions for dual of c-bessel mappings.we show that for a c-bessel mapping $f$, a retrievalformula with respect to a c-bessel mapping $g$ is satisfied if andonly if $g$ is sum of the canonical dual of $f$ with a c-besselmapping which  wea...

In this paper we study the duality of Bessel and g-Bessel sequences in Hilbert spaces. We show that a Bessel sequence is an inner summand of a frame and the sum of any Bessel sequence with Bessel bound less than one with a Parseval frame is a frame. Next we develop this results to the g-frame situation.

he class of generalized Bessel potentials is the main object study in this article. The potential a negative real power operator (I − Δγ), where Δγ = (...)∂xk - Laplace operator, γ (γ1,...,γn) multi-index consisting positive fixed numbers. When solving various problems for differential equations, proving embedding theorems some classes functions, and inverting integral operators, there need to ...