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Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a…
Gradient flow has proved useful in the definition and measurement of renormalized quantities on the lattice. Recently, the fact that it suppresses high-modes of the field has been used to construct new, continuous RG transformations both…
We systematically find conditions which yield locally uniform convergence in the Fourier inversion formula in one and higher dimensions. We apply the gained knowledge to the complex inversion formula of the Laplace transform to extend known…
An important class of fractional differential and integral operators is given by the theory of fractional calculus with respect to functions, sometimes called $\Psi$-fractional calculus. The operational calculus approach has proved useful…
In the paper we consider models of generalized counting processes time-changed by a general inverse subordinator, we characterize their distributions and present governing equations for them. The equations are given in terms of the…
In this note the Chernoff Theorem is used to approximate evolution semigroups constructed by the procedure of subordination. The considered semigroups are subordinate to some original, unknown explicitly but already approximated by the same…
Hermite subdivision schemes act on vector valued data that is not only considered as functions values in $\mathbb{R}^r$, but as consecutive derivatives, which leads to a mild form of level dependence of the scheme. Previously, we have…
The Gr\"unwald and shifted Gr\"unwald formulas for the function $y(x)-y(b)$ are first order approximations for the Caputo fractional derivative of the function $y(x)$ with lower limit at the point $b$. We obtain second and third order…
In this article, we introduce two families of novel fractional $\theta$-methods by constructing some new generating functions to discretize the Riemann-Liouville fractional calculus operator $\mathit{I}^{\alpha}$ with a second order…
We establish interior and up to the boundary H\"older regularity estimates for weak solutions of the Dirichlet problem for the fractional $g-$Laplacian with bounded right hand side and $g$ convex. These are the first regularity results…
The main aim of this paper is to describe the most adequate generalization of the Cauchy-Riemann system fixing properties of classical functions in octonionic case. An octonionic generalization of the Laplace transform is introduced.…
We extend the standard notion of self-concordance to non-convex optimization and develop a family of second-order algorithms with global convergence guarantees. In particular, two function classes -- \textit{weakly self-concordant}…
Functions with uniform sublevel sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used in multicriteria optimization, decision theory, mathematical…
We study operators that are generalizations of the classical Riemann-Liouville fractional integral, and of the Riemann-Liouville and Caputo fractional derivatives. A useful formula relating the generalized fractional derivatives is proved,…
Some general properties of perturbed (rational) CFT in the background metric of symmetric 2D sphere of radius $R$ are discussed, including conformal perturbation theory for the partition function and the large $R$ asymptotic. The truncated…
We consider several notions of regularity, including strong regularity, bounded relative units, and Ditkin's condition, in the setting of vector-valued function algebras. Given a commutative Banach algebra $A$ and a compact space $X$, let…
The Cauchy problem for fractional derivatives linear systems of ordinary differential equations with constant coefficients is considered, where at first the analytic expressions are given through the matrix exponent of its corresponding…
We prove weighted estimates for the maximal regularity operator. Such estimates were motivated by boundary value problems. We take this opportunity to study a class of weak solutions to the abstract Cauchy problem. We also give a new proof…
Matrix functions are utilized to rewrite smooth spectral constrained matrix optimization problems as smooth unconstrained problems over the set of symmetric matrices which are then solved via the cubic-regularized Newton method. A…
Some Caputo q-fractional difference equations are solved. The solutions are expressed by means of a new introduced generalized type of q-Mittag-Leffler functions. The method of successive approximation is used to obtain the solutions. The…