相关论文: Regular and Completely Regular Differential Operat…
Inverse spectral problems are studied for the second order integro-differential operators on a finite interval. Properties of spectral characteristic are established, and the uniqueness theorem is proved for this class of inverse problems.
We introduce three types of partial fractional operators of variable order. An integration by parts formula for partial fractional integrals of variable order and an extension of Green's theorem are proved. These results allow us to obtain…
We give a natural notion of (non-exact) integral functor in the context of k-linear and graded categories. In this broader sense, we prove that every k-linear and graded functor is integral.
The Green functions of the partial differential operators of even order acting on smooth sections of a vector bundle over a Riemannian manifold are investigated via the heat kernel methods. We study the resolvent of a special class of…
Let $\sigma(x,\xi) $ be a sufficiently regular function defined on $R^d \times R^d.$ The pseudo-differential operator with symbol $\sigma$ is defined on the Schwartz class by the formula: \[f\to\sigma f(x)=\int_{R^d} \sigma(x,\xi)…
General, especially spectral, features of compact normal operators in quaternionic Hilbert spaces are studied and some results are established which generalize well-known properties of compact normal operators in complex Hilbert spaces.…
We present a method for calculating the results of operation of differential operators operating on components of vector in generalized coordinates not restricted to orthogonal one. For this we use the relationships between covariant,…
The operators of fractional calculus come in many different types, which can be categorised into general classes according to their nature and properties. We conduct a formal study of the class known as weighted fractional calculus and its…
We introduce a class of (tuples of commuting) unbounded operators on a Banach space, admitting smooth functional calculi, that contains all operators of Helffer-Sj\"ostrand type and is closed under the action of smooth proper mappings.…
The operator product expansion in four-dimensional superconformal field theory is discussed. The OPE takes a particularly simple form for chiral operators, in $N=1$ and $N=2$, and for analytic operators, in $N=2$ and $N=4$. It is argued…
Reduction operators, i.e. the operators of nonclassical (or conditional) symmetry of a class of variable coefficient nonlinear wave equations with power nonlinearities is investigated within the framework of singular reduction operator. A…
We review the D-formalism, a new method for determining the renormalization of Green functions to all orders in perturbation theory. This formalism exploits the fact that the renormalized Green functions may be calculated by displacing by…
Let $A$ and $B$ be two -non necessarily bounded- normal operators. We give new conditions making their product normal. We also generalize a result by Deutsch et al on normal products of matrices.
In this paper, we characterize complementable operators and provide more precise expressions for the Schur complement of these operators using a single Douglas solution. We demonstrate the existence of subspaces where the given operator is…
In this paper, we study the consequences of the fundamental theorem of calculus from an algebraic point of view. For functions with singularities, this leads to a generalized notion of evaluation. We investigate properties of such…
We discuss 1-dimensional Schrodinger operators with complex and locally integrable potentials that may have an arbitrary behavior at (finite or infinite) endpoints. The main tool of our analysis are Green's operators, that is, their various…
We define the concept of higher order differential operators on a general noncommutative, nonassociative superalgebra A, and show that a vertex operator superalgebra has plenty of them, namely modes of vertex operators. A linear operator…
The notion of singular reduction operators, i.e., of singular operators of nonclassical (conditional) symmetry, of partial differential equations in two independent variables is introduced. All possible reductions of these equations to…
For the ring of differential operators on a smooth affine algebraic variety $X$ over a field of characteristic zero a finite set of algebra generators and a finite set of defining relations are found explicitly. As a consequence, a finite…
This paper studies the solvability of a class of Dirichlet problem associated with non-linear integro-differential operator. The main ingredient is the probabilistic construction of continuous supersolution via the identification of the…