Characterizations of distributional weights for weak orthogonal polynomials satisfying a second-order differential equation
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| 024 | 7 | 0 | |a 10.1007/s10231-014-0422-6 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10231-014-0422-6 | ||
| 100 | 1 | |a Lee |D D. |u Department of Mathematics, Teachers College, Kyungpook National University, 702-701, Daegu, South Korea |4 aut | |
| 245 | 1 | 0 | |a Characterizations of distributional weights for weak orthogonal polynomials satisfying a second-order differential equation |h [Elektronische Daten] |c [D. Lee] |
| 520 | 3 | |a Let $$\{ P_n(x) \}_{n=0}^\infty $$ { P n ( x ) } n = 0 ∞ be a monic weak orthogonal polynomial system (weak OPS) of order $$m$$ m relative to $$ \sigma $$ σ . Then we first prove that $$ \sigma $$ σ satisfies a new moment equation 0.1 $$\begin{aligned} P_{m+1} (x) \sigma =0, \end{aligned}$$ P m + 1 ( x ) σ = 0 , and then we find a general representation of $$\sigma $$ σ from the moment equation (0.1). Assuming moreover that $$\{ P_n(x) \}_{n=0}^\infty $$ { P n ( x ) } n = 0 ∞ satisfies a second-order differential equation, we find a distributional representation of $$ \sigma $$ σ for such weak OPSs by the coefficients $$\ell _i$$ ℓ i 's and the eigenvalues $$\lambda _k$$ λ k of differential equation. By analyzing those moment equations thoroughly, we finally classify all moment functionals $$ \sigma $$ σ for the weak OPSs satisfying a second-order differential equation. | |
| 540 | |a Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 | ||
| 690 | 7 | |a Weak orthogonal polynomial |2 nationallicence | |
| 690 | 7 | |a Recurrence relations |2 nationallicence | |
| 690 | 7 | |a Differential equation |2 nationallicence | |
| 690 | 7 | |a Orthogonalizing weights |2 nationallicence | |
| 773 | 0 | |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/5(2015-10-01), 1319-1348 |x 0373-3114 |q 194:5<1319 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-014-0422-6 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10231-014-0422-6 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Lee |D D. |u Department of Mathematics, Teachers College, Kyungpook National University, 702-701, Daegu, South Korea |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/5(2015-10-01), 1319-1348 |x 0373-3114 |q 194:5<1319 |1 2015 |2 194 |o 10231 | ||