A p-adic Schrödinger-type operator Dα +VY is studied. D α (α > 0) is the operator of fractional differentiation and VY = ∑n i,j=1 bij < δxj , · > δxi (bij ∈ C) is a singular potential containing the Dirac delta functions δx concentrated on a set of points Y = {x1, . . . , xn} of the field of p-adic numbers Qp. It is shown that such a problem is well-posed for α > 1/2 and the singular perturbati...

We apply the generalized Jordan sets techniques to reduce partial differential-operator equations with the Fredholm operator in the main expression to regular problems. In addition this techniques has been exploited to prove a theorem of existence and uniqueness of a singular initial problem, as well as to construct the left and right regularizators of singular operators in Banach spaces and to...

In this paper, the reduced dierential transform method is investigated fora nonlinear partial dierential equation modeling nematic liquid crystals, itis called the Hunter-Saxton equation. The main advantage of this methodis that it can be applied directly to nonlinear dierential equations withoutrequiring linearization, discretization, or perturbation. It is a semi analytical-numerical method t...

1 OPERATOR DECOMPOSITIONS In this lecture we will consider two basic decompositions of operators that will be used repeatedly in the course: the spectral decomposition and the singular-value decomposition. The spectral decomposition holds only for normal operators, while the singular-value decomposition holds for all operators. The singular-value decomposition will be particularly important in ...