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- W2084450508 abstract "Let {L () (x)} n⩾0 be the sequence of monic Laguerre matrix polynomials defined on [0, ∞) by $$L_n ^{(A,lambda )} (x) = frac{{n!}}{{( - lambda )^n }}sumlimits_{k = 0}^n {frac{{( - lambda )^k }}{{k!(n - k)!}}(A + I)_n [(A + I)_k ]^{ - 1} x^k } ,$$ where A ∈ C r×r . It is known that {L () (x)} n⩾0 is orthogonal with respect to a matrix moment functional when A satisfies the spectral condition that Re(z) > −1 for every z ∈ σ(A). In this note we show that for A such that σ(A) does not contain negative integers, the Laguerre matrix polynomials L () (x) are orthogonal with respect to a non-diagonal Sobolev-Laguerre matrix moment functional, which extends two cases: the above matrix case and the known scalar case." @default.
- W2084450508 created "2016-06-24" @default.
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- W2084450508 date "2007-03-01" @default.
- W2084450508 modified "2023-09-25" @default.
- W2084450508 title "A note on Sobolev orthogonality for Laguerre matrix polynomials" @default.
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- W2084450508 doi "https://doi.org/10.1007/s10496-001-0026-z" @default.
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