and Applied Analysis 3 As application, we consider the holomorphic case and we prove the following result: Theorem 1.3. We suppose that P is aC0-contraction holomorphic semigroup on B and β be a Bochner subordinator satisfying ∫1 0 1 s βt ds < ∞, t > 0. 1.9 Then each zero-integrable P-exit law ψ is subordinated to a unique P-exit law φ. Moreover, φ is given by φt ( q a ) PtVq ( ψ ) − bAPtVq(ψ) ...

If X is a topological space, and for m ≥ n the maps πm,n : X → X are defined by (πm,n(x))(j) = x(j), j ∈ {1, . . . , n}, then the spaces X and maps πm,n constitute a projective system, and its limit in the category of topological spaces is XN with the maps πn : X N → X, where XN has the initial topology for the family {πn : n ∈ N} (namely, the product topology). We say that a function f : XN → ...

The article proposes a method for analyzing the Cauchy problem wide class of evolutionary linear partial differential equations with variable coefficients. By applying (inverse) Fourier transform, original equation is reduced to an integro-differential equation, which can be considered as ordinary in corresponding Banach space. selection this space carried out such way that principle contractio...

A weak-type inequality is proved for Bochner-Riesz means at the critical index, for functions in L(R), 1 ≤ p < 4/3.

The Bochner-Riesz means are shown to have either the unit interval [0, 1] or the whole complex plane as their spectra on Lp, 1 ≤ p <∞

The continuity of integral kernels related to Schrödinger operators (the kernel of the heat equation, Green’s function) plays an important role in the study of different properties of quantum systems. In the Euclidean case, it was shown in [1] that sufficiently general functions of the Schrödinger operator have continuous integral kernels for scalar potentials belonging to the Kato class. In [2...

Let $T$ be a linear operator that, for some $p_1\in(1,\infty)$, is bounded on $L^{p_1}(\tilde w)$ all $\tilde w\in A_{p_1}(\mathbb R^d)$ and in addition compact $L^{p_1}(w_1)$ $w_1\in R^d)$. Then $L^p(w)$ $p\in(1,\infty)$ $w\in A_p(\mathbb This "compact version" of Rubio de Francia's celebrated weighted extrapolation theorem follows from combination results the interpolation theory spaces one h...