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Full-Text Articles in Mathematics
Pursuing Analogies Between Differential Equations And Difference Equations, David L. Abrahamson
Pursuing Analogies Between Differential Equations And Difference Equations, David L. Abrahamson
Faculty Publications
The study of ordinary differential equations has long been a staple in mathematics at both the undergraduate and graduate levels. Recently, instruction in the study of difference equations has widened, primarily due to the expanded role of the digital computer in mathematics. The two topics are inextricably linked at all levels, from elementary techniques through current research questions. Pursuing the analogies between these fields of study can only deepen the understanding of each. In particular, the study of many elementary topics in difference equations, requiring not even the use of calculus, can serve as a founda- tion for intuition and …
Mat 751 Algebraic Topology I - Fall '89, David Handel
Mat 751 Algebraic Topology I - Fall '89, David Handel
Mathematics Faculty Research Publications
A collection of notes for the course Mat 751, Algebraic Topology I, prepared by Professor David Handel of the Wayne State University Mathematics Department. The notes include examples, exercises, and additional lecture notes on related concepts.
Dilatations Des Commutants D'Opérateurs Pour Des Espaces De Krein De Fonctions Analytiques, Daniel Alpay
Dilatations Des Commutants D'Opérateurs Pour Des Espaces De Krein De Fonctions Analytiques, Daniel Alpay
Mathematics, Physics, and Computer Science Faculty Articles and Research
Let K1 and K2 be two Krein spaces of functions analytic in the unit disk and invariant for the left shift operator R0(R0f(z)=(f(z)−f(0))/z), and let A be a linear continuous operator from K1 into K2 whose adjoint commutes with R0. We study dilations of A which preserve this commuting property and such that the Hermitian forms defined by I−AA∗ and I−BB∗ have the same number of negative squares. We thus obtain a version of the commutant lifting theorem in the framework of Krein spaces of analytic functions. To prove this result we suppose that the graph of the operator A∗, …