On Generalized Stone’s Theorem

An Lp-Lq-version Of Morgan's Theorem For The Generalized Fourier Transform Associated with a Dunkl Type Operator

The aim of this paper is to prove new quantitative uncertainty principle for the generalized Fourier transform connected with a Dunkl type operator on the real line. More precisely we prove An Lp-Lq-version of Morgan's theorem.

k-Nearest Neighbour Classification of Datasets with a Family of Distances

The k-nearest neighbour (k-NN) classifier is one of the oldest and most important supervised learning algorithms for classifying datasets. Traditionally the Euclidean norm is used as the distance for the k-NN classifier. In this thesis we investigate the use of alternative distances for the k-NN classifier. We start by introducing some background notions in statistical machine learning. We defi...

ar X iv : 0 80 9 . 05 38 v 1 [ m at h . L O ] 3 S ep 2 00 8 BOOLEAN ALGEBRAS AND LOGIC

In this article we investigate the notion and basic properties of Boolean algebras and prove the Stone’s representation theorem. The relations of Boolean algebras to logic and to set theory will be studied and, in particular, a neat proof of completeness theorem in propositional logic will be given using Stone’s theorem from Boolean algebra. We mention here that the method we used can also be e...

Stone’s Theorem and Applications

GENERALIZATION OF TITCHMARSH'S THEOREM FOR THE GENERALIZED FOURIER-BESSEL TRANSFORM

In this paper, using a generalized translation operator, we prove theestimates for the generalized Fourier-Bessel transform in the space L2 on certainclasses of functions.