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The Symmetric Meixn...
The Symmetric Meixner-Pollaczek polynomials
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- Araaya, Tsehaye, 1962- (författare)
- Uppsala universitet,Matematiska institutionen
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Kaijser, Sten (preses)
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Janson, Svante (preses)
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- Rosengren, Hjalmar, Assistant professor (opponent)
- Mathematics, Göteborg
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(creator_code:org_t)
- ISBN 9150616811
- Uppsala : Matematiska institutionen, 2003
- Engelska 13 s.
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Serie: Uppsala Dissertations in Mathematics, 1401-2049 ; 27
- Relaterad länk:
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https://uu.diva-port... (primary) (Raw object)
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Abstract
Ämnesord
Stäng
- The Symmetric Meixner-Pollaczek polynomials are considered. We denote these polynomials in this thesis by pn(λ)(x) instead of the standard notation pn(λ) (x/2, π/2), where λ > 0. The limiting case of these sequences of polynomials pn(0) (x) =limλ→0 pn(λ)(x), is obtained, and is shown to be an orthogonal sequence in the strip, S = {z ∈ ℂ : −1≤ℭ (z)≤1}.From the point of view of Umbral Calculus, this sequence has a special property that makes it unique in the Symmetric Meixner-Pollaczek class of polynomials: it is of convolution type. A convolution type sequence of polynomials has a unique associated operator called a delta operator. Such an operator is found for pn(0) (x), and its integral representation is developed. A convolution type sequence of polynomials may have associated Sheffer sequences of polynomials. The set of associated Sheffer sequences of the sequence pn(0)(x) is obtained, and is foundto be ℙ = {{pn(λ) (x)} =0 : λ ∈ R}. The major properties of these sequences of polynomials are studied.The polynomials {pn(λ) (x)}∞n=0, λ < 0, are not orthogonal polynomials on the real line with respect to any positive real measure for failing to satisfy Favard’s three term recurrence relation condition. For every λ ≤ 0, an associated nonstandard inner product is defined with respect to which pn(λ)(x) is orthogonal. Finally, the connection and linearization problems for the Symmetric Meixner-Pollaczek polynomials are solved. In solving the connection problem the convolution property of the polynomials is exploited, which in turn helps to solve the general linearization problem.
Ämnesord
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Nyckelord
- Mathematical analysis
- Meixner-Pollaczek polynomial
- Orthogonal polynomial
- Polynomial operator
- Inner product
- Umbral calculus
- Sheffer polynomial
- Convolution type polynomial
- Connection and linearization problem
- 33C45
- 05A40
- 33D45
- Matematisk analys
- Mathematical analysis
- Analys
- matematik
- Mathematics
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