We prove exponential decay for the solution of the Schrödinger equation on a dissipative waveguide. The absorption is effective everywhere on the boundary but the geometric control condition is not satisfied. The proof relies on separation of variables and the Riesz basis property for the eigenfunctions of the transverse operator. The case where the absorption index takes negative values is als...

We constructively prove (i.e., in ZF set theory) a decomposition theorem for certain order bounded disjointness preserving operators between any two Riesz spaces, real or complex, in terms of the absolute value of another order bounded disjointness preserving operator. In this way, we constructively generalize results by Abramovich, Arensen and Kitover (1992), Grobler and Huijsmans (1997), Hart...

In this paper the localization properties of the spectral expansions of distributions related to the self adjoint extension of the Schrodinger operator are investigated. Spectral decompositions of the distributions and some classes of distributions are defined. Estimations for Riesz means of the spectral decompositions of the distributions in the norm of the Sobolev classes with negative order ...

where x, u and y are the system state, input and output, respectively, A is a densely defined differential linear operator on an (infinite-dimensional) Hilbert space (e.g., L(a, b), a, b ∈ R), which generates a C0-semigroup, and B, C and D are bounded linear operators. Moreover, if A is a Riesz-spectral operator, it possesses several interesting properties, regarding in particular observability...

Results analogous to those proved by Rubio de Francia [28] are obtained for a class of maximal functions formed dilations bilinear multiplier operators limited decay. We focus our attention on L2 × → L1 estimates. discuss two applications: the boundedness Bochner-Riesz operator and spherical operator. For latter we improve known results in [1] reducing dimension restriction from n ≥ 8 4.

We prove weighted norm inequalities for fractional powers of elliptic operators together with their commutators with BMO functions, encompassing what is known for the classical Riesz potentials and elliptic operators with Gaussian domination by the classical heat operator. The method relies upon a good-λ method that does not use any size or smoothness estimates for the kernels.

We prove weighted norm inequalities for fractional powers of elliptic operators together with their commutators with BMO functions, encompassing what is known for the classical Riesz potentials and elliptic operators with Gaussian domination by the classical heat operator. The method relies upon a good-λ method that does not use any size or smoothness estimates for the kernels.

An operator T ∈ B(H) is called quasi ∗-paranormal if ||T ∗Tx||2 ≤ ||T x|||Tx|| for all x ∈ H. If μ is an isolated point of the spectrum of T , then the Riesz idempotent E of T with respect to μ is defined by

Let E ⊂ Rn+1, n ≥ 2, be an Ahlfors-David regular set of dimension n. We show that the weak-A∞ property of harmonic measure, for the open set Ω := Rn+1 \ E, implies uniform rectifiability of E. More generally, we establish a similar result for the Riesz measure, p-harmonic measure, associated to the p-Laplace operator, 1 < p < ∞.