A simple analytic formula for the spectral radius of matrix continuous refinement operators is established. On the space L2 (R),m ≥ 1 and s ≥ 1, their spectral radius is equal to the maximal eigenvalue in magnitude of a number matrix, obtained from the dilation matrix M and the matrix function c defining the corresponding refinement operator. A similar representation is valid for the continuous...

We consider a generalization of isometric Hilbert space operators to the multivariable setting. We study some of the basic properties of these tuples of commuting operators and we explore several examples. In particular, we show that the d-shift, which is important in the dilation theory of d-contractions (or row contractions), is a d-isometry. As an application of our techniques we prove a the...

Mathematical morphology is based on the algebraic framework of complete lattices and adjunctions, which endows it with strong properties and allows for multiple extensions. In particular, extensions to fuzzy sets of the main morphological operators, such as dilation and erosion, can be done while preserving all properties of these operators. Another, more recent, extension, concerns bipolar fuz...

We construct monopole operators for 3d Yang-Mills-matter theories and Chern-Simons-matter in canonical formalism. In this framework, operators, although as the disorder could be written terms of fundamental fields theory, thus treated same way ordinary operators. study properties constructed theories, transform local with classical conformal dimension $ 0 under action dilation are also covarian...

BACKGROUND Transnasal cannulation of the natural ostium in patients with an intact uncinate process is complicated by the lack of direct visualization of the ostium. Accuracy of transnasal dilation of the maxillary ostium was evaluated for a malleable-tipped balloon device that was bent to specific angles for avoiding the fontanelle during cannulation. METHODS Transnasal cannulation and dila...

Let Pf(x) = −if ′(x) and Qf(x) = xf(x) be the canonical operators acting on an appropriate common dense domain in L2(R). The derivations DP (A) = i(PA−AP ) and DQ(A) = i(QA−AQ) act on the ∗-algebra A of all integral operators having smooth kernels of compact support, for example, and one may consider the noncommutative “Laplacian” L = D2 P + D 2 Q as a linear mapping of A into itself. L generat...

The paper is devoted to the problem of exact calculation norms in ideal spaces for monotone operators on cones functions with monotonicity properties. We implement a general approach this that covers many concrete variants and different conditions functions. As applications, we calculate some integral cones, associate over Lebesgue spaces, dilation operator embedding weighted Lorentz weights. U...

Identifying the salient zones fromWeb interfaces, namely the Website Key Objects, is an essential part of the personalization process that current Web systems perform to increase user engagement. While several techniques have been proposed, most of them are focused on the use of Web usage logs. Only recently has the use of data from users' biological responses emerged as an alternative to enric...

1. This note is a continuation of our earlier paper [-3], in which we developed a dilation theory for a certain class of contraction operators acting on a separable, infinite dimensional, complex Hilbert space ~ . The notation and terminology in what follows is taken from [3]. For the convenience of the reader we recall a few pertinent definitions. The algebra of bounded linear operators on ~ i...