Related papers: A sufficient condition for global operator monoton…
Continuing previous work, this paper focuses on the summability problem of multivariate rational functions in the mixed case in which both shift and $q$-shift operators can appear. Our summability criteria rely on three ingredients…
In this paper we solve Kolmogorov problem about existence of a function with given norms of derivatives for classes of multiple monotone functions and absolute monotone functions in the case of arbitrary number of norms. We also show the…
In this expository article, we discuss various monotonicity formulas for parabolic and elliptic operators and explain how the analysis of the function spaces and the geometry of the underlining spaces are intertwined. After briefly…
We consider generalized definitions of mixing and exactness for random dynamical systems in terms of Markov operator cocycles. We first give six fundamental definitions of mixing for Markov operator cocycles in view of observations of the…
The comonotonic maxitivity property of functionals frequently appears in the characterization of fuzzy integrals based on the maximum operation. In some special cases, comonotonic maxitivity implies monotonicity of functionals. The question…
An elementary, but very useful lemma due to Biernacki and Krzy\.{z} (1955) asserts that the ratio of two power series inherits monotonicity from that of the sequence of ratios of their respective coefficients. Over the last two decades it…
Conditions when application of cyclization procedure does not lead to the periodic function are specified. Sufficient conditions under which obtained function is periodic are stated.
We give necessary and sufficient conditions for a pair of (generalized) functions $\rho_1(\mathbf{r}_1)$ and $\rho_2(\mathbf{r}_1,\mathbf{r}_2)$, $\mathbf{r}_i\in X$, to be the density and pair correlations of some point process in a…
We give a sufficient condition for subelliptic estimates for the d-bar-Neumann operator on smoothly bounded, pseudoconvex domains in $\mathbb{C}^n$. This condition is a quantified version of McNeal's condition ($\tilde{P}$) for compactness…
The aim of this paper is first to give necessary and sufficient condition of existence (of free boundaries) for both Laplacian and bi-Laplacian operators in the case where the overdetermined condition is not constant. second, by using some…
In this brief note, we show that the hypotheses of L\"owner's theorem on matrix monotonicity in several commuting variables as proved by Agler, McCarthy and Young can be significantly relaxed. Specifically, we extend their theorem from…
We study stochastic monotonicity and propagation of order for Markov processes with respect to stochastic integral orders characterized by cones of functions satisfying $\Phi f \geq 0$ for some linear operator $\Phi$. We introduce a new…
In this paper we introduce a very general setting dealing with the superposition of operators of any positive order and provide a systematic study of them. We also provide examples and counterexamples, as well as characterizing properties…
We introduce different classical characteristics used to regularize a subharmonic function and compare them. As an application we give a complete proof of a useful characterization of the modulus of continuity of such functions in terms of…
We prove that the functions t -> (t^q-1)(t^p-1)^{-1} are operator monotone in the positive half-axis for 0 < p < q < 1, and we calculate the two associated canonical representation formulae. The result is used to find new monotone metrics…
This paper identifies necessary and sufficient conditions for the exactness of penalty functions in optimization problems whose constraint sets are not necessarily bounded. The case where the data of problems is locally Lipschitz,…
We improve constants in the Rademacher-Menchov inequality.
We provide sufficient conditions of local solvability for partial differential operators with variable Colombeau coefficients. We mainly concentrate on operators which admit a right generalized pseudodifferential parametrix and on operators…
For a broad class of integral functionals defined on the space of $n$-dimensional convex bodies, we establish necessary and sufficient conditions for monotonicity, and necessary conditions for the validity of a Brunn-Minkowski type…
The convergence of a new general variable metric algorithm based on compositions of averaged operators is established. Applications to monotone operator splitting are presented.