Abstract We introduce differential primary decompositions for ideals in a commutative ring. Ideal membership is characterized by conditions. The minimal number of conditions needed the arithmetic multiplicity. Minimal are unique up to change bases. Our results generalize construction Noetherian operators analytic theory Ehrenpreis–Palamodov, and they offer concise method representing affine sch...

This paper is devoted to the proof of the unique solvability ofthe inverse problems for second-order differential operators withregular singularities. It is shown that the potential functioncan be determined from spectral data, also we prove a uniquenesstheorem in the inverse problem.

We give an algorithm to write down all conformally invariant differential operators acting between scalar functions on Minkowski space. All operators of order k are nonlinear and are functions on a finite family of functionally independent invariant operators of order up to k. The independent differential operators of second order are three and we give an explicit realization of them. The appli...

We discuss the concept of what we refer to as semi-commuting linear differential operators. Such operators hold commuting operators as a special case. In particular, we discuss a heuristic by which one may construct such operators. Restricting to the case in which one such operator is of degree two, we construct families of linear differential operators semi-commuting with some named operators ...

We shall show that every differential operator of 2-nd order in a real separable Hilbert space can be decomposed into a regular and an irregular operator. Then we shall characterize irregular operators and differential operators satisfying the maximum principle. Results obtained for the Lévy laplacian in [3] will be generalized for irregular differential operators satisfying the maximum principle.

We give an algorithm write down all conformally invariant differential operators acting between scalar functions on Minkowski space. All operators of order k are nonlinear and are functions on a finite family of functionally independent invariant operators of order up to k. The independent differential operators of second order are three and we give an explicit realization of them. The applied ...

An atomic decomposition is considered in Banach space.  A method for constructing an atomic decomposition of Banach  space, starting with atomic decomposition of  subspaces  is presented. Some relations between them are established. The proposed method is used in the  study  of the  frame  properties of systems of eigenfunctions and associated functions of discontinuous differential operators.

‎in this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular sturm-liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎also weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...

In this paper, the optimal conditions for fractional optimal control problems (FOCPs) were derived in which the fractional differential operators defined in terms of Caputo sense and reduces this problem to a system of fractional differential equations (FDEs) that is called twopoint boundary value (TPBV) problem. An approximate solution of this problem is constructed by using the Legendre-Gauss...

We present a new approach for expressing and solving boundary problems for linear ordinary differential equations in the language of differential algebras. Starting from an algebra with a derivation and integration operator, we construct a ring of linear integro-differential operators that is expressive enough for specifying regular boundary problems with arbitrary Stieltjes boundary conditions...