COMPLETENESS OF THE EXPONENTIAL SYSTEM ON A SEGMENT OF THE REAL AXIS
Gaisin A.M. Kanguzhin B.E. Seitova A.A.
2022L.N. Gumilyov Eurasian National University
Eurasian Mathematical Journal
2022#13Issue 237 - 42 pp.
Let Λ = {λn} be the sequence of all zeros of the entire function (Formula Presented) of exponential type. We consider exponential system of functions (Formula Presented), where mn-is the multiplicity of the zero λn. The question is: for which a, b (a < b) is the system e(Λ) complete (incomplete) in the space L2(a,b)? Let D be the length of the indicator conjugate diagram of the entire function Δ(λ). Then the following statements are valid: • when b - a > D the system e(Λ) is incomplete in L2(a,b); • when b - a < D the system e(Λ) is complete in L2(a,b); • if we remove from Λ any two points λ and μ, then the system e(Ω),Ω = Λ/{λ,μ} is incomplete in L2(a,b) also when b - a = D
Beurling-malliavin multiplier theorem , Borel adjoint diagram , Cartwright class , Indicatrix of the growth , Lebesgue-stieltjes integral , Paley-wiener theorem
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Institute of Mathematics with Computing Centre, Subdivision of the Ufa Federal Research Centre of the Russian Academy of Sciences, Bashkir State University, 112 Chernyshevsky St, Ufa, 450008, Russian Federation
Al-Farabi Kazakh National University, 71 al-Farabi Ave, Almaty, 050040, Kazakhstan
Institute of Mathematics and Mathematical Modeling, 125 Pushkin St, Almaty, 050010, Kazakhstan
Institute of Mathematics with Computing Centre
Al-Farabi Kazakh National University
Institute of Mathematics and Mathematical Modeling
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