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Trumping Preemption
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متن کاملHyperbolic Polynomials and the Dirichlet Problem
This paper presents a simple, self-contained account of G̊arding’s theory of hyperbolic polynomials, including a recent convexity result of Bauschke-Guler-Lewis-Sendov and an inequality of Gurvits. This account also contains new results, such as the existence of a real analytic arrangement of the eigenvalue functions. In a second, independent part of the paper, the relationship of G̊arding’s theo...
متن کاملHarmonic Polynomials and Dirichlet-Type Problems
We take a new approach to harmonic polynomials via differentiation. Surprisingly powerful results about harmonic functions can be obtained simply by differentiating the function |x|2−n and observing the patterns that emerge. This is one of our main themes and is the route we take to Theorem 1.7, which leads to a new proof of a harmonic decomposition theorem for homogeneous polynomials (Corollar...
متن کاملConvergence of Dirichlet Polynomials in Banach Spaces
Recent results on Dirichlet series ∑ n an 1 ns , s ∈ C, with coefficients an in an infinite dimensional Banach space X show that the maximal width of uniform but not absolute convergence coincides for Dirichlet series and for m-homogeneous Dirichlet polynomials. But a classical non-trivial fact due to Bohnenblust and Hille shows that if X is one dimensional, this maximal width heavily depends o...
متن کاملDirichlet orthogonal polynomials with Laguerre weight
Let {λj}j=1 be a sequence of distinct positive numbers. We find explicit formulae for the orthogonal Dirichlet polynomials {ψn} formed from linear combinations of { λ−it j }n j=1 , associated with the Laguerre weight. Thus ∫ ∞ 0 ψn (t)ψm (t)e −tdt = δmn. In addition, we estimate Christoffel functions and establish Markov-Bernstein inequalities.
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2013
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/46/22/225302