Bases occurring in the solution of equations of mixed type (Q2704025)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bases occurring in the solution of equations of mixed type |
scientific article |
Statements
8 April 2002
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nonharmonic analysis
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system of exponentials
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multiplier
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Riesz basis
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sine-type function
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Bases occurring in the solution of equations of mixed type (English)
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Let \((\lambda_n)^\infty_{n=0}\) be a separable sequence of all roots of some sine-type function \(L(z)\). If \(L(x)\) is a multiplier of class \((L^p,L^p)\), \(2< p<\infty\), then the system \((e^{i\lambda_nt}, te^{i\lambda_nt},\dots, t^{m_n- 1} e^{i\lambda_nt})^\infty_{n= 0}\), where \(m_n\) is a multiplicite of a root \(\lambda_n\), is a Riesz basis in \(L^p(-\pi, \pi)\).
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