Related papers: Projection Operator Approach to Constrained System…

We study contractive projections, isometries, and real positive maps on algebras of operators on a Hilbert space. For example we find generalizations and variants of certain classical results on contractive projections on C*-algebras and…

Motivated by practical applications, I present a novel and comprehensive framework for operator-valued positive definite kernels. This framework is applied to both operator theory and stochastic processes. The first application focuses on…

In many instances one has to deal with parametric models. Such models in vector spaces are connected to a linear map. The reproducing kernel Hilbert space and affine- / linear- representations in terms of tensor products are directly…

New integrable boundary conditions for integrable quantum systems can be constructed by tuning of scattering phases due to reflection at a boundary and an adjacent impurity and subsequent projection onto sub-spaces. We illustrate this…

Iterative hybrid projection methods have proven to be very effective for solving large linear inverse problems due to their inherent regularizing properties as well as the added flexibility to select regularization parameters adaptively. In…

We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves…

In this article we consider means of positive bounded linear operators on a Hilbert space. We present a complete theory that provides a framework which extends the theory of the Karcher mean, its approximating matrix power means, and a…

This paper studies the eigenvalue problem $K \psi = \lambda \psi$ associated with a Fredholm integral operator $K$ defined by a smooth kernel. The focus is on analyzing the convergence behaviour of numerical approximations to eigenvalues…

Motivated by the entropic optimal transport problem in unbounded settings, we study versions of Hilbert's projective metric for spaces of integrable functions of bounded growth. These versions of Hilbert's metric originate from cones which…

We present an embedding of stochastic optimal control problems, of the so called path integral form, into reproducing kernel Hilbert spaces. Using consistent, sample based estimates of the embedding leads to a model free, non-parametric…

Optimization under structural constraints is typically analyzed through projection or penalty methods, obscuring the geometric mechanism by which constraints shape admissible dynamics. We propose an operator-theoretic formulation in which…

In this paper we study the convergence of an iterative algorithm for finding zeros with constraints for not necessarily monotone set-valued operators in a reflexive Banach space. This algorithm, which we call the proximal-projection method…

This paper presents reproducing kernel Hilbert spaces method to obtain the numerical solution for partial differential equation constrained optimization problem.

Computing reduced-order models using non-intrusive methods is particularly attractive for systems that are simulated using black-box solvers. However, obtaining accurate data-driven models can be challenging, especially if the underlying…

We generalize some aspects of the theory of compact projections relative to a C*-algebra, to the setting of more general algebras. Our main result is that compact projections are the decreasing limits of `peak projections', and in the…

Contrary to the traditional pursuit of research on nonuniform sampling of bandlimited signals, the objective of the present paper is not to find sampling conditions that permit perfect reconstruction, but to perform the best possible signal…

We introduce and analyze an abstract algorithm that aims to find the projection onto a closed convex subset of a Hilbert space. When specialized to the fixed point set of a quasi nonexpansive mapping, the required sufficient condition…

Conventional vision algorithms adopt a single type of feature or a simple concatenation of multiple features, which is always represented in a high-dimensional space. In this paper, we propose a novel unsupervised spectral embedding…

We derive a new expansion of the Heisenberg equation of motion based on the projection operator method proposed by Shibata, Hashitsume and Shing\=u. In their projection operator method, a certain restriction is imposed on the initial state.…

This thesis is concerned with retrodiction and measurement in quantum optics. The latter of these two concepts is studied in particular form with a general optical multiport device, consisting of an arbitrary array of beam-splitters and…