Let L := −r−2(r∂r )2 − ∂2 z . We consider the equation Lu = f on a bounded polygonal domain with suitable boundary conditions, derived from the three-dimensional axisymmetric Poisson’s equation. We establish the well-posedness, regularity, and Fredholm results in weighted Sobolev spaces, for possible singular solutions caused by the singular coefficient of the operator L, as r → 0, and by non-s...

Let X be a Spin manifold with boundary, such that the Spin structure is defined near the boundary by an almost complex structure, which is either strictly pseudoconvex or pseudoconcave (and hence contact). Using generalized Szego projectors, we define modified partial differential-Neumann boundary conditions, Reo, for spinors, which lead to subelliptic Fredholm boundary value problems for the S...

Let L := −r−2(r∂r)2 − ∂2 z . We consider the equation Lu = f on a bounded polygonal domain with suitable boundary conditions, derived from the three-dimensional axisymmetric Poisson’s equation. We establish the well-posedness, regularity and Fredholm results in weighted Sobolev spaces, for possible singular solutions caused by the singular coefficient of the operator L, as r → 0, and by non-smo...

Continuing a line of investigation initiated in [11] exploring the connections between Jost and Evans functions and (modified) Fredholm determinants of Birman–Schwinger type integral operators, we here examine the stability index, or sign of the first nonvanishing derivative at frequency zero of the characteristic determinant, an object that has found considerable use in the study by Evans func...

We show that the Fredholm spectrum of an evolution semigroup {E}t≥0 is equal to its spectrum, and prove that the ranges of the operator Et − I and the generator G of the evolution semigroup are closed simultaneously. The evolution semigroup is acting on spaces of functions with values in a Banach space, and is induced by an evolution family that could be the propagator for a well-posed linear d...

This paper presents direct settings and rigorous solutions of the main Statistical Inference problems. It shows that rigorous solutions require solving multidimensional Fredholm integral equations of the first kind in the situation where not only the right-hand side of the equation is an approximation, but the operator in the equation is also defined approximately. Using Stefanuyk-Vapnik theory...

We give a short proof of the theorem of Brown, Douglas and Fillmore that an essentially normal operator on a Hilbert space is a compact perturbation of a normal operator if and only if the Fredholm index of its translates are zero whenever deened. The proof is a modiication of the short proof of Lin's theorem on almost commuting self-adjoint elements we gave in 7]. Using similar methods we prov...

The main purpose of this article is to give a relationship between Fredholm multivalued linear operators and the demicompact relation; we provide some sufficient conditions on inputs closable block operator matrix ensure generalized demicompactness its closure. Our results generalize many known ones in literature.