Related papers: Spectral calculations on locally convex vector spa…
We use the functorial properties of Rieffel's pseudodifferential calculus to study families of operators associated to topological dynamical systems acted by a symplectic space. Information about the spectra and the essential spectra are…
We establish sharp bounds for simultaneous local rotation and H\"older-distortion of planar quasiconformal maps. In addition, we give sharp estimates for the corresponding joint quasiconformal multifractal spectrum, based on new estimates…
This article gives dual representations for convex integral functionals on the linear space of regular processes. This space turns out to be a Banach space containing many more familiar classes of stochastic processes and its dual can be…
In this paper, we systematically investigate the multidimensional $Z$-transform of functions with values in sequentially complete locally convex spaces over the field of complex numbers. We provide many structural characterizations, remarks…
The article deals with operations defined on convex polyhedra or polyhedral convex functions. Given two convex polyhedra, operations like Minkowski sum, intersection and closed convex hull of the union are considered. Basic operations for…
We obtain some new characterizations of a variable version of Lipschitz spaces in terms of the boundedness of commutators of sharp maximal functions, fractional maximal functions or fractional maximal commutators in the context of the…
The $\epsilon$-subdifferential of convex univariate piecewise linear-quadratic functions can be computed in linear worst-case time complexity as the level-set of a convex function. Using dichotomic search, we show how the computation can be…
In this note we review some recent results concerning integral representation properties of local functionals driven by Lipschitz continuous anisotropies.
Some mathematical models of applied problems lead to the need of solving boundary value problems with a fractional power of an elliptic operator. In a number of works, approximations of such a nonlocal operator are constructed on the basis…
We consider positive, integral-preserving linear operators acting on $L^1$ space, known as stochastic operators or Markov operators. We show that, on finite-dimensional spaces, any stochastic operator can be approximated by a sequence of…
In the symbol space for differential operators, we discuss a scalar type for change of local coordinates, using vector valued distributions. In particular, we discuss P-convexity for hypoelliptic operators.
We introduce the sketch of construction of a Lipschitz function $f: \mathcal{C} \to H$, here the set $\mathcal{C}$ consists of all compact convex subsets of the Hadamard space $H$. Note that $f(\{x\})=\{x\}$ for any point $x \in H$.
We present a formula for the interpolation of matrix weighted spaces of vector valued functions via interpolation functors. We apply our formula to the particular case of interpolation of matrix weighted $L^p$ spaces by the real and complex…
Explicit solutions of differential equations of complex fractional orders with respect to functions and with continuous variable coefficients are established. The representations of solutions are given in terms of some convergent infinite…
The approximation of functions in Orlicz space by multivariate operators on simplex is considered. The convergence rate is given by using modulus of smoothness.
In this paper we provide a definition of fractional gradient operators, related to directional derivatives. We develop a fractional vector calculus, providing a probabilistic interpretation and mathematical tools to treat multidimensional…
In this paper we consider some properties of the initial logarithmic coefficients for inverse functions of functions univalent in the unit disc. The case of convex functions is treated separately. We give estimate, in some cases sharp, of…
This article gives a fundamental discussion on variable coefficients, self-adjoint, formally partially hypoelliptic differential operators. A generalization of the results to pseudo differential operators, is given in a following article in…
We prove quadratic estimates for complex perturbations of Dirac-type operators, and thereby show that such operators have a bounded functional calculus. As an application we show that spectral projections of the Hodge--Dirac operator on…
In the present note a functional calculus $\phi \mapsto \phi(A)$ for self-adjoint definitizable linear relation on Krein spaces is developed. This functional calculus is the proper analogue of $\phi \mapsto \int \phi \, dE$ in the Hilbert…