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On The Characterization Of Finite Dimensional Hida Distributions., Kyoung Sim Lee
On The Characterization Of Finite Dimensional Hida Distributions., Kyoung Sim Lee
LSU Historical Dissertations and Theses
The mathematical framework of white noise analysis is based on an infinite dimensional analogue of the Schwartz distribution theory. The Lebesgue measure on $\IR\sp{k}$ is replaced with standard Gaussian measures $\mu$ on infinite dimensional spaces. There is an infinite dimensional analogue $({\cal E})\subset L\sp2({\cal E}\sp*,\mu)\subset({\cal E})\sp*$ of a Gel'fand triple ${\cal E}\subset E\subset{\cal E}\sp*$ which is obtained from ${\cal S}(\IR\sp{k})\subset L\sp2(\IR\sp{k})\subset{\cal S}\sp*(\IR\sp{k})$ in a general setup. There are spaces $({\cal E}\sp\beta),({\cal E}\sp\beta)\sp*, \beta\in\lbrack 0,1)$ with $({\cal E}\sp\beta)\subset({\cal E})\subset L\sp2({\cal E}\sp*,\mu)\subset({\cal E})\sp*\subset({\cal E}\sp\beta)\sp*.$. The compositions of Schwartz distributions and Gaussian random variables have been discussed. A new Gel'fand triple ${\cal H}(\IR\sp{k})\subset{\cal …
Split Abelian Extensions Of Calgebras., Mark Andrew Curole
Split Abelian Extensions Of Calgebras., Mark Andrew Curole
LSU Historical Dissertations and Theses
It is shown that the C* algebra of a groupoid with Haar system has a natural split abelian extension. For a split abelian extension of a C* algebra it is shown that all representations of the original algebra extend to the split abelian extension. Under a reasonable assumption it is shown that states extend to a split abelian extension. Definitions for quasi-invariant and ergodic measures are given for split abelian extension of C* algebras, and it is shown when the split abelian extension is the natural extension of the C* algebra of a groupoid with Haar system that these definitions …
Linkage By Generically Gorenstein Cohen-Macaulay Ideals., Heath Mayall Martin
Linkage By Generically Gorenstein Cohen-Macaulay Ideals., Heath Mayall Martin
LSU Historical Dissertations and Theses
In a Gorenstein local ring R, two ideals A and B are said to be linked by an ideal I if the two relations A = (I: B) and B = (I: A) hold. In the case that I is a complete intersection, or a Gorenstein ideal, it is known that linkage preserves the Cohen-Macaulay property. That is, if A is a Cohen-Macaulay ideal, then so is B. However, if I is allowed to be a generically Gorenstein, Cohen-Macaulay ideal, easy examples show that this type of linkage does not preserve the Cohen-Macaulay property. The primary purpose of this work …
The Congruence Extension Property, The Ideal Extension Property, And Ideal Semigroups., Karen Dommert Aucoin
The Congruence Extension Property, The Ideal Extension Property, And Ideal Semigroups., Karen Dommert Aucoin
LSU Historical Dissertations and Theses
A semigroup has the congruence extension property (CEP) provided that each congruence on each subsemigroup of S extends to a congruence on S. The ideal extension property (IEP) for semigroups is defined analogously. A characterization of commutative semigroups with IEP is given in terms of multiplicative conditions within and between the archimedean components of the semigroup. A similar characterization of commutative semigroups with CEP is sought. Toward this end, archimedean semigroups with CEP are characterized in terms of multiplicative structure and a number of necessary conditions on multiplication between the archimedean components of a commutative semigroup with CEP are established. …
The Congruence Extension Property And Related Topics In Semigroups., Jill Ann Dumesnil
The Congruence Extension Property And Related Topics In Semigroups., Jill Ann Dumesnil
LSU Historical Dissertations and Theses
A semigroup has the congruence extension property (CEP) provided that each congruence on each subsemigroup can be extended to a congruence on the semi-group. This property, the ideal extension property (IEP), and other related concepts are studied from both an algebraic and a topological perspective in this work. A characterization of semigroups with CEP is given in terms of the lattice of congruences. A similar result is obtained for IEP. Semigroups in which the relation "is an ideal of" is transitive (t-semigroups) are explored. It is shown that each of CEP and IEP implies this condition and that these are …