Translation and convolution associated with discrete wavelet transform are investigated using properties of Calderón-Zygmund operator and Riesz fractional integral operator. Dual convolution is also studied. The wavelet convolution is applied to approximate functions belonging to certain p L-spaces.

In this paper, we study the generation problem of Riesz basis for a general network of strings with joint damping at each vertex. First, we give a basic spectral property of the system operator A. Under certain conditions, we prove that the spectrum of A is distributed in a strip parallel to the imaginary axis. By the discussion of the completeness of generalized eigenvectors of the operator A,...

Riesz potentials of fractal measures μ in metric spaces and their inverses are introduced . They define self–adjoint operators in the Hilbert space L2(μ) and the former are shown to be compact. In the Euclidean case the corresponding spectral asymptotics are derived with Besov space methods. The inverses of the Riesz potentials are fractal pseudodifferential operators. For the order two operato...


 En este trabajo X es un espacio de Banach y B(X) denota los operadores acotados. Si T∈B(X), por lat(T) entenderemos subespacios invariantes T. Se dice que T lleno, si (T(M)) ̅=M, para todo M∈lat(T) (la barra indica la clausura en topología inducida norma). prueba principalmente el siguiente resultado: Sean ∈B(X) acotado abajo. Sea K ∈Alglat(T)∩{T}' operador Riesz. entonces lleno. Aquí Alg...

In the present paper, we shall give necessary and sufficient conditions for the strong and weak boundedness of the Riesz potential operator [Formula: see text] on Orlicz spaces. Cianchi (J. Lond. Math. Soc. 60(1):247-286, 2011) found necessary and sufficient conditions on general Young functions Φ and Ψ ensuring that this operator is of weak or strong type from [Formula: see text] into [Formula...

A Timoshenko beam equation with boundary feedback control is considered. By an abstract result on the Riesz basis generation for the discrete operators in the Hilbert spaces, we show that the closed-loop system is a Riesz system, that is, the sequence of generalized eigenvectors of the closed-loop system forms a Riesz basis in the state Hilbert space. 1. Introduction. The boundary feedback stab...

The boundedness of Bessel–Riesz operators defined on Lebesgue spaces and Morrey in measure metric is discussed this research study. maximal operator traditional dyadic decomposition are used to study the Bessel-Riesz operators. We investigate interaction between kernel space parameters get results see how affects kernel-bound

In this work we established asymptotical behavior for Riesz means of the spectral function of the Laplace operator on unit sphere.

We establish two inequalities of Stein-Weiss type for the Riesz potential operator Iα,γ (B−Riesz potential operator) generated by the Laplace-Bessel differential operator ΔB in the weighted Lebesgue spaces Lp,|x|β ,γ . We obtain necessary and sufficient conditions on the parameters for the boundedness of Iα,γ from the spaces Lp,|x|β ,γ to Lq,|x|−λ ,γ , and from the spaces L1,|x|β ,γ to the weak...