A continuous linear Hilbert space operator S is said to be a 2-isometry if the and its adjoint S∗ satisfy relation S∗2S2−2S∗S+I=0. We study operators having liftings or dilations 2-isometries. The of an which admits such restriction backward shift on vector-valued analytic functions. These results are applied concave similar contractions. Two types 2-isometries, as well extensions induced by th...

We extend a result of Coifman and Dahlberg [Singular integral characterizations of nonisotropic H spaces and the F. and M. Riesz theorem, Proc. Sympos. Pure Math., Vol. 35, pp. 231–234; Amer. Math. Soc., Providence, 1979] on the characterization of H spaces by singular integrals of R with a nonisotropic metric. Then we apply it to produce singular integral versions of generalized BMO spaces. Mo...

The relationship between multiresolution analysis and filtering schemes is a well-known facet of wavelet theory. However, in the case of rational dilation factors, the wavelet literature is somewhat lacking in its treatment of this relationship. This work seeks to establish a means for the construction of stable filtering schemes with rational dilations through the theory of shift-invariant spa...

The zone of root hair formation of seedling radish roots, Raphanus sativus L., was studied by phase-contrast and electron microscopy. Localized dilations of the endoplasmic reticulum, which contained a moderately dense proteinaceous material, were found to be a common component of the cytoplasm in cells of the epidermis and cortex. The surfaces of these dilations were covered with polyribosomes...

In the first part, we recall the axiomatic definition of the elementary morphological operators (dilations, erosions, anti–dilations and anti–erosions) and their characterization in the case of Boolean lattices. This characterization is used to derive the set operator decompositions from the general decompositions of operators between complete lattices. In the second part, we define the notions...

Strictures of the urethra are the most common cause of obstructed micturition in younger men and there is frequent recurrence after initial treatment. Currently, routine repeated dilations, including intermittent self-catheterisation (ISC) are prescribed by urologists to prevent urethral stricture recurrence. There is, however, no high level evidence available supporting the effectiveness of pr...