In this paper, the algebraic, geometric and analytic multiplicities of an eigenvalue for linear differential operators are defined and classified. The relationships among three multiplicities of an ...

ABSTRACT: In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ...

Linear operators form the cornerstone of analysis in Banach spaces, offering a framework in which one can rigorously study continuity, spectral properties and stability. Banach space theory, with its ...

SIAM Journal on Applied Mathematics, Vol. 42, No. 5 (Oct., 1982), pp. 941-955 (15 pages) Slepian, Landau and Pollak found that a certain finite convolution integral operator on the real line commutes ...

We study the solutions of ordinary linear differential equations whose coefficients are analytic elements. As one application we show nonexistence of index for certain linear differential operators ...

Abstract: We show that linear differential operators with polynomial coefficients over a field of characteristic zero can be multiplied in quasi-optimal time. This answers an open question raised by ...

Abstract: A surface-current equivalence theorem that states that the electromagnetic fields outside a three-dimensional (3-D) source region can be generated (to any degree of accuracy) by electric and ...

An annihilator, in the context of differential equations, is a differential operator that, when applied to a given function, yields zero. More formally, if L is a differential operator and f(x) is a ...

Pseudodifferential operators serve as a pivotal extension of classical differential operators by incorporating non-local features through their symbols. These operators are fundamental in the analysis ...