Observe that H 0 (M) = L p(M). Also, Hk := H2 k is a Hilbert space under the L2-inner product. F k contains only smooth functions. In general, a sequence in F k will not converge in the H k norm to a function in F k , so we need to complete the space to have anything useful. An alternate approach would have been to start with functions in Lp rather than completing the space of smooth functions ...

We consider a random variable Y and approximations Yn, n ∈ N, defined on the same probability space with values in the same measurable space as Y . We are interested in situations where the approximations Yn allow to define a Dirichlet form in the space L (PY ) where PY is the law of Y . Our approach consists in studying both biases and variances. The article attempts to propose a general theor...

We present an algorithm that solves the following motion-planning problem. Given an L-shaped body L and a 2-dimensional region with n point obstacles, decide whether there is a continuous motion connecting two given positions and orientations of L during which L avoids collision with the obstacles. The algorithm requires O(n 2 log 2 n) time and O(n 2) storage. The algorithm is a variant of the ...

Abstract. Invariance principle in L(0, 1) is studied using signed random measures. This approach to the problem uses an explicit isometry between L(0, 1) and a reproducing kernel Hilbert space giving a very convenient setting for the study of compactness and convergence of the sequence of Donsker functions. As an application, we prove a L(0, 1) version of the invariance principle in the case of...

In this paper, we developed a novel approach that provides effective and robust segmentation of color images. It preprocesses an image by converting color information from RGB to CIE L*a*b* color spaces that CIE L*a*b* color spaces can express color in a device-independent way. CIE L*a*b* color space is better suited to digital image manipulations than the RGB space, because it had removed corr...

The BFT approach is used to formulate the electronic states in graphene through a non-commutative space in the presence of a constant magnetic field B for the first time. In this regard, we introduce a second class of constrained system, which is not gauge symmetric but by applying BFT method and extending phase space, the second class constraints  converts  to the first class constraints so th...

MOTIVATION Sequence alignment is the problem of finding the optimal character-by-character correspondence between two sequences. It can be readily solved in O(n2) time and O(n2) space on a serial machine, or in O(n) time with O(n) space per O(n) processing elements on a parallel machine. Hirschberg's divide-and-conquer approach for finding the single best path reduces space use by a factor of n...

We give an operator theoretic approach to the constructions of multiresolutions as they are used in a number of basis constructions with wavelets, and in Hilbert spaces on fractals. Our approach starts with the following version of the classical Baumslag-Solitar relations ut = tu where t is a unitary operator in a Hilbert space H and u is an isometry in H. There are isometric dilations of this ...

We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...