Lipschitz Continuity of the Absolute Value and Riesz Projections in Symmetric Operator Spaces

Lipschitz Continuity of inf-Projections

It is shown that local epi-sub-Lipschitz continuity of the function-valued mapping associated with a perturbed optimization problem yields the local Lipschitz continuity of the inf-projections (= marginal functions, = infimal functions). The use of the theorem is illustrated by considering perturbed nonlinear optimization problems with linear constraints.

Absolute Continuity of Symmetric Markov Processes

We study Girsanov’s theorem in the context of symmetric Markov processes, extending earlier work of Fukushima-Takeda and Fitzsimmons on Girsanov transformations of “gradient type”. We investigate the most general Girsanov transformation leading to another symmetric Markov process. This investigation requires an extension of the forward-backward martingale method of Lyons-Zheng, to cover the cas...

Oblique Projections, Biorthogonal Riesz Bases and Multiwavelets in Hilbert Spaces

In this paper, we obtain equivalent conditions relating oblique projections to biorthogonal Riesz bases and angles between closed linear subspaces of a Hilbert space. We also prove an extension theorem in the biorthogonal setting, which leads to biorthogonal multiwavelets.

Absolute Continuity of the Periodic Magnetic Schrödinger Operator

We prove that the spectrum of the Schrödinger operator with periodic electric and magnetic potentials is absolutely continuous.

Absolute Continuity and Singularity of Probability Measures in Functional Spaces