On strongly condensing operators

Φ-strongly Accretive Operators

Suppose that X is an arbitrary real Banach space and T : X → X is a Lipschitz continuous φ-strongly accretive operator or uniformly continuous φ-strongly accretive operator. We prove that under different conditions the three-step iteration methods with errors converge strongly to the solution of the equation Tx = f for a given f ∈ X.

Some Random Fixed Point Theorems for Condensing and Nonexpansive Operators

Some random versions of deterministic fixed point theorems for condensing and nonexpansive operators are obtained.

On Spectral Theory for Schrödinger Operators with Strongly Singular Potentials

We examine two kinds of spectral theoretic situations: First, we recall the case of self-adjoint half-line Schrödinger operators on [a,∞), a ∈ R, with a regular finite end point a and the case of Schrödinger operators on the real line with locally integrable potentials, which naturally lead to Herglotz functions and 2× 2 matrix-valued Herglotz functions representing the associated Weyl–Titchmar...

Strongly Singular Convolution Operators on the Heisenberg Group

We consider the L mapping properties of a model class of strongly singular integral operators on the Heisenberg group H; these are convolution operators on H whose kernels are too singular at the origin to be of Calderón-Zygmund type. This strong singularity is compensated for by introducing a suitably large oscillation. Our results are obtained by utilizing the group Fourier transform and unif...

Inequalities for Strongly Singular Convolution Operators