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Full-Text Articles in Analysis
A Dilation Theoretic Approach To Approximation By Inner Functions, Daniel Alpay, Tirthankar Bhattacharyya, Abhay Jindal, Poornendu Kumar
A Dilation Theoretic Approach To Approximation By Inner Functions, Daniel Alpay, Tirthankar Bhattacharyya, Abhay Jindal, Poornendu Kumar
Mathematics, Physics, and Computer Science Faculty Articles and Research
Using results from the theory of operators on a Hilbert space, we prove approximation results for matrix-valued holomorphic functions on the unit disc and the unit bidisc. The essential tools are the theory of unitary dilation of a contraction and the realization formula for functions in the unit ball of . We first prove a generalization of a result of Carathéodory. This generalization has many applications. A uniform approximation result for matrix-valued holomorphic functions which extend continuously to the unit circle is proved using the Potapov factorization. This generalizes a theorem due to Fisher. Approximation results are proved for matrix-valued …
Perturbation - For Nature Computes On A Straight Line (In Seven Balancing Acts), Vijay Fafat
Perturbation - For Nature Computes On A Straight Line (In Seven Balancing Acts), Vijay Fafat
Journal of Humanistic Mathematics
What if all of our Reality is a simulation? What, perhaps, are the unintended artifacts if we are an "approximate" simulation because God could not muster sufficient computational power for the Equations capturing the ultimate Theory of Everything? Are life and Sentience something She intended, a problem with the simulation's code, or an irreducible, teleological inevitability in Creation?
New Characterizations Of Reproducing Kernel Hilbert Spaces And Applications To Metric Geometry, Daniel Alpay, Palle E. T. Jorgensen
New Characterizations Of Reproducing Kernel Hilbert Spaces And Applications To Metric Geometry, Daniel Alpay, Palle E. T. Jorgensen
Mathematics, Physics, and Computer Science Faculty Articles and Research
We give two new global and algorithmic constructions of the reproducing kernel Hilbert space associated to a positive definite kernel. We further present a general positive definite kernel setting using bilinear forms, and we provide new examples. Our results cover the case of measurable positive definite kernels, and we give applications to both stochastic analysis and metric geometry and provide a number of examples.
Gaussian Guesswork: Infinite Sequences And The Arithmetic-Geometric Mean, Janet Heine Barnett
Gaussian Guesswork: Infinite Sequences And The Arithmetic-Geometric Mean, Janet Heine Barnett
Calculus
No abstract provided.
Approximation Of Solutions To The Mixed Dirichlet-Neumann Boundary Value Problem On Lipschitz Domains, Morgan F. Schreffler
Approximation Of Solutions To The Mixed Dirichlet-Neumann Boundary Value Problem On Lipschitz Domains, Morgan F. Schreffler
Theses and Dissertations--Mathematics
We show that solutions to the mixed problem on a Lipschitz domain Ω can be approximated in the Sobolev space H1(Ω) by solutions to a family of related mixed Dirichlet-Robin boundary value problems which converge in H1(Ω), and we give a rate of convergence. Further, we propose a method of solving the related problem using layer potentials.