We reformulate the original component-by-component algorithm for rank-1 lattices in a matrix-vector notation so as to highlight its structural properties. For function spaces similar to a weighted Korobov space, we derive a technique which has construction cost O(sn log(n)), in contrast

I have been blessed with many wonderful people around me in this journey towards my doctoral degree. First and foremost, I would like to thank my adviser, Dr. Vern I. Paulsen, for all his contribution of time, ideas, insightful comments, and funding in this pursuit of mine. It was an honor and pleasure to work under his guidance. I just hope that some day I can be as good a mathematician as him. Next, I would like to thank my thesis committee members, Dr. David P. Blecher, Dr. Bernhard G. Bodmann, and Dr. David Sherman, for careful reading of my thesis, helpful suggestions, and ideas for future projects. I greatly acknowledge the financial, academic, and technical support from my department, the Department of Mathematics at the University of Houston. I would like to thank all the members of my department for building a friendly, helpful, and excellent research environment to work. I thank all my teachers at the Mathematical Sciences Foundation (MSF) and University of Delhi for training me in various foundational areas of Mathematics. I extend my special thanks to Dr. Sanjeev Agrawal, Dr. Amber Habib, and Dr.

Abstract: We review definitions and properties of reproducing kernel Hilbert spaces attached to Gaussian variables and processes, with a view to applications

entirely on parametric approaches. This places fundamental limits on the kind of policies that can be represented. In this work, we show how policy search (with or without the additional guidance of value-functions) in a Reproducing Kernel Hilbert Space gives a simple and rigorous extension

A reproducing kernel Hilbert space (RKHS) has four well-known easily derived properties. Since these properties are usually not emphasized as a simple means of gaining insight into RKHS structure, they are singled out and proved here.

Abstract. We introduce a reproducing kernel structure for Hilbert spaces of functions where differences of point evaluations are bounded. The associ-ated reproducing kernels are characterized in terms of conditionally negative functions. 1.

This paper introduces a generalized cross-correlation (GCC) measure for spike train analysis derived from reproducing kernel Hilbert spaces (RKHS) theory. An estimator for GCC is derived that does not depend on binning or a specific kernel and it operates directly and efficiently on spike times

The inner product in RKHS is described in abstract form. Some of the results, published earlier, are discussed from a general point of view. In particular, the characterization of the range of linear integral transforms and inversion formulas, announced in the works of Saitoh, are analyzed.

de recherche ISSN 0249-6399 ISRN INRIA/RR--6908--FR+ENGA General Framework for Nonlinear Functional

that I have read this thesis and that in my opinion it is fully adequate,