by Yu Wai-kuen. / Thesis (M. Phil.)--Chinese University of Hong Kong, 1981. / Bibliography: l. 52-55.

Dans cette thèse, nous avont pre'esent'e un schéma général de dualité pour des problèmes d'inéquations variationnelles monotones. Ce schéma est analogue le schéma classique de dualité dans la programmation convexe en ajoutant des variables de perturbation. Afin d'arriver à cet objectif, avant nous avons approfondi quelques propriétés et caractérisations des multi-applications (sous-ensemble) monotones et maximal monotones sur un point de vue global et local. En particulier, nous donnons un algorithme pour construire une extension maximal monotone d'une multi-application monotone (sous-ensemble) arbitraire. Nous avons spécifiquement étudié les sous-espaces affine monotone. Dans ce cas particulier, la construction d'une extension maximal monotone peut être construit par un nombre fini d'étapes. Finalement, des applications de notre schéma de dualité quelques classes des problèmes d'inéquations variationnels sont discutées.

<p>This thesis consists of three parts. The first part is a introduction to the theory of domains of holomorphy through holomorphic convexity. The second part gives a introduction to Stein neighborhood bases in <strong>C</strong>ⁿ<strong> </strong>and presents some minor results on the Nebenhülle of a compact set in <strong>C</strong>ⁿ. The third and final part reviews some results on the existence of Stein neighborhood bases.</p> / <p>Denna uppsats består av tre delar. Den första delen introducerar holomorfiområden genom teorin för konvexitet med avseende på holomorfa funktioner. Den andra delen är en introduktion till Steinomgivningsbaser i <strong>Cⁿ</strong> och presenterar några smärre resultat rörande Nebenhüllet till en kompakt mängd i <strong>Cⁿ</strong>. Den tredje och sista delen ger en överblick över en del resultat om existensen av Steinomgivningsbaser.</p>

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, August 1997. / Includes bibliographical references. Also available on the Internet.

This thesis consists of three parts. The first part is a introduction to the theory of domains of holomorphy through holomorphic convexity. The second part gives a introduction to Stein neighborhood bases in Cn and presents some minor results on the Nebenhülle of a compact set in Cn. The third and final part reviews some results on the existence of Stein neighborhood bases. / Denna uppsats består av tre delar. Den första delen introducerar holomorfiområden genom teorin för konvexitet med avseende på holomorfa funktioner. Den andra delen är en introduktion till Steinomgivningsbaser i Cn och presenterar några smärre resultat rörande Nebenhüllet till en kompakt mängd i Cn. Den tredje och sista delen ger en överblick över en del resultat om existensen av Steinomgivningsbaser.

No description available.

This thesis is an investigation of the sequence of functions defined by fl (x) -xand fn+1 (x) -x , where the power is the principal value.In the case where the sequence is restricted to positive real this sequence of functions over thecomplex plane, we attack real numbers, the problem yields to the methods of analysis and we prove the behavior of the sequence.The more general problem of describing the behavior of both analytically and numerically. Though no full rigorous solution is given, the results presented suggest the behavior of the sequence over the complex plane is very interesting. / Department of Mathematical Sciences

Thesis (Ph. D.)--University of Rhode Island, 2003. / Typescript. Includes bibliographical references (leaves 154-158).

In this thesis we consider problems related to rational inner functionsand several different Hilbert spaces on the unit polydisc. In the general introduction the functions and the function spaces we will be interested in are introduced, and in particular we point outproblems and phenomena that occur in higher dimensions and are notpresent for one variable functions. For example, we provide a detailed construction of a non-trivial shift-invariant subspace of Dirichlet-type spaces on the bidisc which is not fnitely generated. Furthermore, Clark-Aleksandrov measures are generalized to higher dimensions, and certain results about such measures are proved. Paper I concerns containment of rational inner functions in Dirichlet-type spaces on polydiscs. In particular a theorem relating H^p integrability of the partial derivatives of a rational inner function to containment of the function in certain Dirichlet-type spaces is proved. As a corollary, we see that every rational inner function on D^n belongs to the isotropic Dirichlet-type space with weight 1/n. In Paper II, Zhu's sub-Bergman spaces of one variable functions on the unit disc are generalized to weighted Bergman spaces on D^n. Unlike in one variable,we show that sub-Bergman spaces associated to a rational inner function are generally not contained in a weighted Bergman space of higher regularity. We also show how Clark measures on the n-torus can be used to study model spaces on D^n associated to rational inner functions.

No description available.