The vector-valued big q-Jacobi transform

Big $q$-Jacobi functions are eigenfunctions of a second order $q$-difference operator $L$. We study $L$ as an unbounded self-adjoint operator on an $L^2$-space of functions on $\mathbb R$ with a discrete measure. We describe explicitly the spectral decomposition of $L$ using an integral transform $\mathcal F$ with two different big $q$-Jacobi functions as a kernel, and we construct the inverse of $\mathcal F$.Comment: 35 pages, corrected an error and typo

Asymmetric cycloaddition reactions between 2-benzopyrylium-4-olates and 3-(2-alkenoyl)-2-oxazolidinones in the presence of 2,6-bis(oxazolinyl)pyridine-lanthanoid complexes

ArticleTetrahedron. 62(39): 9218-9225 (2006)journal articl

PREPARATION OF NEW NITROGEN-BRIDGED HETEROCYCLES. 63. UNEXPECTED FORMATION OF THIENO[3 ',4 ':4,5]IMIDAZO[1,2-a]-PYRIDINES

The alkaline treatment and dehydrogenation of pyridinium salts, obtainable from the S-alkylation of 3,5-dimethylpyridinium 2-alkylthio-1-cyano2-thioxoethylides with some phenacyl bromides, afforded unexpected heterocycles, 3-alkylthio-1-arylcarbonyl-6,8-dimethylthieno[3',4':4,5]imidazo-[1,2-a]pyridines, together with the corresponding 2-alkylthio-1-arylcarbonylthio-6,8-dimethylindolizine-3-carbonitriles.ArticleHETEROCYCLES. 76(1): 391-399 (2008)journal articl

A solution to the Al-Salam--Chihara moment problem

We study the $q$-hypergeometric difference operator $L$ on a particular Hilbert space. In this setting $L$ can be considered as an extension of the Jacobi operator for $q^{-1}$-Al-Salam--Chihara polynomials. Spectral analysis leads to unitarity and an explicit inverse of a $q$-analog of the Jacobi function transform. As a consequence a solution of the Al-Salam--Chihara indeterminate moment problem is obtained.Comment: 22 page

Splines and Wavelets on Geophysically Relevant Manifolds

Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two decades, the importance of these and other applications triggered the development of various tools such as splines and wavelet bases suitable for the unit spheres $\mathbb{S}^{2}$, $\>\>\mathbb{S}^{3}$ and the rotation group $SO(3)$. Present paper is a summary of some of results of the author and his collaborators on generalized (average) variational splines and localized frames (wavelets) on compact Riemannian manifolds. The results are illustrated by applications to Radon-type transforms on $\mathbb{S}^{d}$ and $SO(3)$.Comment: The final publication is available at http://www.springerlink.co

Expert consensus document: Semantics in active surveillance for men with localized prostate cancer — results of a modified Delphi consensus procedure

Active surveillance (AS) is broadly described as a management option for men with low-risk prostate cancer, but semantic heterogeneity exists in both the literature and in guidelines. To address this issue, a panel of leading prostate cancer specialists in the field of AS participated in a consensus-forming project using a modified Delphi method to reach international consensus on definitions of terms related to this management option. An iterative three-round sequence of online questionnaires designed to address 61 individual items was completed by each panel member. Consensus was considered to be reached if ≥70% of the experts agreed on a definition. To facilitate a common understanding among all experts involved and resolve potential ambiguities, a face-to-face consensus meeting was held between Delphi survey rounds two and three. Convenience sampling was used to construct the panel of experts. In total, 12 experts from Australia, France, Finland, Italy, the Netherlands, Japan, the UK, Canada and the USA participated. By the end of the Delphi process, formal consensus was achieved for 100% (n = 61) of the terms and a glossary was then developed. Agreement between international experts has been reached on relevant terms and subsequent definitions regarding AS for patients with localized prostate cancer. This standard terminology could support multidisciplinary communication, reduce the extent of variations in clinical practice and optimize clinical decision making