Gaussian subordination for the Beurling-Selberg extremal problem
By Emanuel Carneiro, Friedrich Littmann, Jeffrey D. Vaaler. 2010
50 citations recorded by the source corpus.
We determine extremal entire functions for the problem of ma- jorizing, minorizing, and approximating the Gaussian function e x 2 by en- tire functions of exponential type. The combination of the Gaussian and a general distribution approach provides the solution of the extremal problem for a wide class of even functions that includes most of the previously known examples (for instance (3), (4), (10) and (17)), plus a variety of new interesting functions such asjxj for 1 < ; log (x 2 + 2 )=(x 2 + 2 ) , for 0 < ; log x2 + 2 ; andx2n logx2 , forn2 N. Further applications to number theory include optimal approximations of theta functions by trigonometric polynomi- als and optimal bounds for certain Hilbert-type inequalities related to the discrete Hardy-Littlewood-Sobolev inequality in dimension one.
Subfields: Algebra and Number Theory, Geometry and Topology, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/68e17c6e939fbbbca47956e1dfaedeb005c01097
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In Algebra and Number Theory
In Geometry and Topology
Citations in the corpus
- The fourth moment of quadratic Dirichlet L-functions over function fields (2016, background): “26 ALEXANDRA FLOREA which is proven in Theorem 4 in [5].”