Related papers: Parameterized splitting theorems and bifurcations …
New splitting theorems in a semi-Riemannian manifold which admits an irrotational vector field (not necessarily a gradient) with some suitable properties are obtained. According to the extras hypothesis assumed on the vector field, we can…
We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficient may depend on space and time. Pointwise convergence of the…
We compare the integration by parts of contact forms - leading to the definition of the interior Euler operator - with the so-called canonical splittings of variational morphisms. In particular, we discuss the possibility of a…
This paper involves generalizing the Goldblatt-Thomason and the Lindstr\"om characterization theorems to first-order modal logic.
Operator splitting methods tailored to coupled linear port-Hamiltonian systems are developed. We present algorithms that are able to exploit scalar coupling, as well as multirate potential of these coupled systems. The obtained algorithms…
We characterize the solutions of the Poisson equation and the domain of its associated one-sided Hilbert transform for Ces\`aro bounded operators of fractional order. The results obtained fairly generalize the corresponding ones for…
The aim of this paper is to get the boundedness of rough sublinear operators generated by fractional integral operators on vanishing generalized weighted Morrey spaces under generic size conditions which are satisfied by most of the…
In this work, we introduce a new generalized integral transform involving many potentially known or new transforms as special cases. Basic properties of the new integral transform, that investigated in this work, include the existence…
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
The construction of rationally-extended Morse potentials is analyzed in the framework of first-order supersymmetric quantum mechanics. The known family of extended potentials $V_{A,B,{\rm ext}}(x)$, obtained from a conventional Morse…
The classical $L^2$ estimate for the $\overline{\partial}$ operators is a basic tool in complex analysis of several variables. Naturally, it is expected to extend this estimate to infinite dimensional complex analysis, but this is a…
The relative index theorem is proved for general first-order elliptic operators that are complete and coercive at infinity over measured manifolds. This extends the original result by Gromov-Lawson for generalised Dirac operators as well as…
We study operator-splitting schemes for approximating Koopman generators of linear semigroups induced by nonlinear flows, a framework originating with Dorroh and Neuberger. Building on ideas of Lie, Kowalewski, and Gr\"{o}bner, we analyze…
In this paper we describe an iterative operator-splitting method for unbounded operators. We derive error bounds for iterative splitting methods in the presence of unbounded operators and semigroup operators. Here mixed applications of…
We develop a framework for a duality theory for general multilinear operators which extends that for transversal multilinear operators which has been established in arXiv:1809.02449. We apply it to the setting of joints and multijoints, and…
Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation.…
This paper consists of four parts. It begins by using the authors's generalized Schauder formula, [50], and the algebraic multiplicity, $\chi$, of Esquinas and L\'opez-G\'omez [18,17,40] to package and sharpening all existing results in…
The survey covers several topics related to the asymptotic structure of various combinatorial and analytic objects such as the path spaces in graded graphs (Bratteli diagrams), invariant measures with respect to countable groups, etc. The…
Motivated by applications in databases, this paper considers various fragments of the calculus of binary relations. The fragments are obtained by leaving out, or keeping in, some of the standard operators, along with some derived operators…
In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained…