Let be a bounded linear operator in a complex separable Hilbert space , and be a selfadjoint operator in . Assuming that belongs to the Schatten-von Neumann ideal
Suppose A is a sectorial operator on a Banach space X, which admits an H∞-calculus. We study conditions on a multiplicative perturbation B of A which ensure that B also has an H∞-calculus. We identify a class of bounded operators T : X→X, which we call strongly triangular, such that if B = (1 + T) A is sectorial then it also has an H∞-calculus. In the case X is a Hilbert space an operator is strongly triangular if and only if ∑ Sn(T)/n <∞ where (Sn(T))n=1∞ are the singular values of T.
We establish new existence results for nontrivial solutions of some integral inclusions of Hammerstein type, that are perturbed with an affine functional. In order to use a theory of fixed point index for multivalued mappings, we work in a cone of continuous functions that are positive on a suitable subinterval of . We also discuss the optimality of some constants that occur in our theory. We improve, complement and extend previous results in the literature.
Let H be a real Hilbert space and T be a maximal monotone operator on H. A well-known algorithm, developed by R. T. Rockafellar [16], for solving the problem (P) ”To find x ∈ H such that 0 ∈ T x” is the proximal point algorithm. Several generalizations have been considered by several authors: introduction of a perturbation, introduction of a variable metric in the perturbed algorithm, introduction of a pseudo-metric in place of the classical regularization, . . . We summarize some of these extensions...
We study a class of rotation invariant determinantal ensembles in the complex plane; examples include the eigenvalues of Gaussian random matrices and the roots of certain families of random polynomials. The main result is a criterion for a central limit theorem to hold for angular statistics of the points. The proof exploits an exact formula relating the generating function of such statistics to the determinant of a perturbed Toeplitz matrix.
In this paper, we introduce Pexiderized generalized operators on certain special spaces introduced by Bielecki-Czerwik and investigate their norms.
We present models of the dynamics of phytoplankton aggregates. We start with an individual-based model in which aggregates can grow, divide, joint and move randomly. Passing to infinity with the number of individuals, we obtain a model which describes the space-size distribution of aggregates. The density distribution function satisfies a non-linear transport equation, which contains terms responsible for the growth of phytoplankton aggregates, their fragmentation, coagulation, and diffusion.
A method is presented for segmenting one-dimensional signal whose independent segments are modeled as polynomials, and which is corrupted by additive noise. The method is based on sparse modeling, the main part is formulated as a convex optimization problem and is solved by a proximal splitting algorithm. We perform experiments on simulated and real data and show that the method is capable of reliably finding breakpoints in the signal, but requires careful tuning of the regularization parameters...