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Full-Text Articles in Physical Sciences and Mathematics
On Compactness And Closed-Rangeness Of Composition Operators, Arnab Dutta
On Compactness And Closed-Rangeness Of Composition Operators, Arnab Dutta
Graduate Theses and Dissertations
Let $\phi$ be an analytic self-map of the unit disk $\mathbb{D}:=\{z:\lvert z\rvert
Conformally Invariant Operators In Higher Spin Spaces, Chao Ding
Conformally Invariant Operators In Higher Spin Spaces, Chao Ding
Graduate Theses and Dissertations
In this dissertation, we complete the work of constructing arbitrary order conformally invariant operators in higher spin spaces, where functions take values in irreducible representations of Spin groups. We provide explicit formulas for them.
We first construct the Dirac operator and Rarita-Schwinger operator as Stein Weiss type operators. This motivates us to consider representation theory in higher spin spaces. We provide corrections to the proof of conformal invariance of the Rarita-Schwinger operator in [15]. With the techniques used in the second order case [7, 18], we construct conformally invariant differential operators of arbitrary order with the target space being degree-1 …
The Maximal Thurston-Bennequin Number On Grid Number N Diagrams, Emily Goins Thomas
The Maximal Thurston-Bennequin Number On Grid Number N Diagrams, Emily Goins Thomas
Graduate Theses and Dissertations
We will prove an upper bound for the Thurston-Bennequin number of Legendrian knots and links on a rectangular grid with arc index n.
TB(n)=CR(n)-[n/2]
In order to prove the bound, we will separate our work for when n is even and when n is odd. After we prove the upper bound, we will show that there are unique knots and links on each grid which achieve the upper bound. When n is even, torus links achieve the maximum, and when n is odd, torus knots achieve the maximum.