Related papers: Effective intervals and regular Dirichlet subspace…
We extensively discuss the Rademacher and Sobolev-to-Lipschitz properties for generalized intrinsic distances on strongly local Dirichlet spaces possibly without square field operator. We present many non-smooth and infinite-dimensional…
Fractional differential and integral operators, Dirichlet averages, and splines of complex order are three seemingly distinct mathematical subject areas addressing different questions and employing different methodologies. It is the purpose…
Real number calculations on elementary functions are remarkably difficult to handle in mechanical proofs. In this paper, we show how these calculations can be performed within a theorem prover or proof assistant in a convenient and highly…
In this paper we give an algebraic construction of the (active) reflected Dirich- let form. We prove that it is the maximal Silverstein extension whenever the given form does not possess a killing part and we prove that Dirichlet forms need…
A new and simple proof of the embedding of the Hardy--Hilbert space of Dirichlet series into a conformally invariant Hardy space of the half-plane is presented, and the optimal constant of the embedding is computed.
In this paper we prove optimal error estimates for {solutions with natural regularity} of the equations describing the unsteady motion of incompressible shear-thinning fluids. We consider a full space-time semi-implicit scheme for the…
We consider symmetric Dirichlet forms on locally compact and non-locally compact spaces and provide an elementary proof for their closability with respect to energy dominant measures. We also discuss how to use known potential theoretic…
In this paper, we study the regularity of $\mathbb{R}$-differentiable functions on open connected subsets of the scaled hypercomplex numbers $\left\{ \mathbb{H}_{t}\right\} _{t\in\mathbb{R}}$ by studying the kernels of suitable differential…
The aim of this paper is to characterize universal and multiplier interpolating sequences for de Branges-Rovnyak spaces H (b) where the defining function b is a general non-extreme rational function. Our results carry over to recently…
The interval approach to computation of dynamics of celestial bodies in the planetary problem has been considered. It is based on the refusal from idealization of infinitely high resolving capacity of measuring tools, and forms an…
We provide the explicit formula for the numerical index of any $2$-dimensional Lipschitz-free space, also giving the construction of operators attaining this value as its numerical radius. As a consequence, the numerical index of…
As is known, the free heat-kernel on the integers (a modified Bessel function) is turned into the periodic free heat-kernel on the discrete circle by factoring, giving a pre-image sum. I generalise existing treatments by making the…
We investigate Dirichlet-type series generated by representation functions that count the number of ways an integer can be expressed as a sum of 'k' signed higher even powers. By combining generalized theta generating functions with a…
Regularity estimates in time and space for solutions to the porous medium equation are shown in the scale of Sobolev spaces. In addition, higher spatial regularity for powers of the solutions is obtained. Scaling arguments indicate that…
Consider a multiply-connected domain $\Sigma$ in the sphere bounded by $n$ non-intersecting quasicircles. We characterize the Dirichlet space of $\Sigma$ as an isomorphic image of a direct sum of Dirichlet spaces of the disk under a…
For a given reciprocal matrix A, we give a union of matrix intervals in which any consistent matrix obtained from an efficient vector for A lies, and, conversely, any consistent matrix in this union comes from an efficient vector for A. The…
The in-out formalism is a systematic and powerful method for finding the effective actions in an electromagnetic field and a curved spacetime provided that the field equation has explicitly known solutions. The effective action becomes…
Some new expressions are found, concerning the effective action as a regularized path-integral for Dirac's spinors in {\it 3+1} dimensions, in the presence of general uniform (i.e., constant and homogeneous) electric and magnetic fields.…
Electronic structure codes usually allow to calculate the work function as a part of the theoretical description of surfaces and processes such as adsorption thereon. This requires a proper calculation of the electrostatic potential in all…
We develop a sharp maximal regularity theory for the resolvent and evolution Stokes equations with no-slip boundary conditions, focusing on bounded domains of low regularity. Our framework covers the full scales of Besov and Sobolev spaces,…