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Full-Text Articles in Harmonic Analysis and Representation
Diederich-Fornæss Index On Boundaries Containing Crescents, Jason Demoulpied
Diederich-Fornæss Index On Boundaries Containing Crescents, Jason Demoulpied
Graduate Theses and Dissertations
The worm domain developed by Diederich and Fornæss is a classic example of a boundedpseudoconvex domains that fails to satisfy global regularity of the Bergman Projection, due to the set of weakly pseudoconvex points that form an annulus in its boundary. We instead examine a bounded pseudoconvex domain Ω ⊂ C2 whose set of weakly pseudoconvex points form a crescent in its boundary. In 2019, Harrington had shown that these types of domains satisfy global regularity of the Bergman Projection based on the existence of good vector fields. In this thesis we study the Regularized Diederich-Fornæss index of these domains, …
Interpolation And Sampling In Analytic Tent Spaces, Caleb Parks
Interpolation And Sampling In Analytic Tent Spaces, Caleb Parks
Graduate Theses and Dissertations
Introduced by Coifman, Meyer, and Stein, the tent spaces have seen wide applications in harmonic analysis. Their analytic cousins have seen some applications involving the derivatives of Hardy space functions. Moreover, the tent spaces have been a recent focus of research. We introduce the concept of interpolating and sampling sequences for analytic tent spaces analogously to the same concepts for Bergman spaces. We then characterize such sequences in terms of Seip's upper and lower uniform density. We accomplish this by exploiting a kind of Mobius invariance for the tent spaces.
Lecture 10: Preconditioned Iterative Methods For Linear Systems, Edmond Chow
Lecture 10: Preconditioned Iterative Methods For Linear Systems, Edmond Chow
Mathematical Sciences Spring Lecture Series
Iterative methods for the solution of linear systems of equations – such as stationary, semi-iterative, and Krylov subspace methods – are classical methods taught in numerical analysis courses, but adapting these methods to run efficiently at large-scale on high-performance computers is challenging and a constantly evolving topic. Preconditioners – necessary to aid the convergence of iterative methods – come in many forms, from algebraic to physics-based, are regularly being developed for linear systems from different classes of problems, and similarly are evolving with high-performance computers. This lecture will cover the background and some recent developments on iterative methods and preconditioning …
Perceiving Mathematics And Art, Edmund Harriss
Perceiving Mathematics And Art, Edmund Harriss
Mic Lectures
Mathematics and art provide powerful lenses to perceive and understand the world, part of an ancient tradition whether it starts in the South Pacific with tapa cloth and wave maps for navigation or in Iceland with knitting patterns and sunstones. Edmund Harriss, an artist and assistant clinical professor of mathematics in the Fulbright College of Arts and Sciences, explores these connections in his Honors College Mic lecture.