On L¹ extremal problem for entire functions

2012/04/20 by Peter Yuditskii, Yuditskii, Peter · 1 citation
Mathematics · #30D15 #30F20 #34K08 #41A30 #41A50 #47B36 #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1204.4620

openalex publication_date 2012/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalized the Korkin-Zolotarev theorem to the case of entire functions having the smallest L¹ norm on a system of intervals E. If \bbC∖ E is a domain of Widom type with the Direct Cauchy Theorem we give an explicit formula for the minimal deviation. Important relations between the problem and the theory of canonical systems with reflectionless resolvent functions are shown.

Citations

• Reflectionless Herglotz functions and generalized Lyapunov exponents

Cited by

• Kotani-Last problem and Hardy spaces on surfaces of Widom type

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