Analogs of Schmidt’s Formula     for Polyorthogonal Polynomials of the First Type

Starovoitov, A. P.; Ryabchenko, N. V.

doi:10.1134/s0001434621090091

Cited by 4 publications

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“…Under some assumption on the "general position" of the tuple (cf. [9], [3], [11]) this construction provides two (m + 1) × (m + 1) polynomial matrices M 1 (z) and M 2 (z), M 1 (z), M 2 (z) ∈ GL(m + 1, C[z]), with the following property: M 1 (z)M 2 (z) ≡ I m+1 , where I m+1 is the identity (m + 1) × (m + 1)-matrix.…”

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On Some Algebraic Properties of Hermite--Padé Polynomials

Suetin¹

2022

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Let [f0, . . . , fm] be a tuple of series in nonnegative powers of 1/z, fj(∞) = 0. It is supposed that the tuple is in "general position". We give a construction of type I and type II Hermite-Padé polynomials to the given tuple of degrees n and mn respectively and the corresponding (m + 1)-multi-indexes with the following property. Let M1(z) and M2(z) be two (m + 1) × (m + 1) polynomial matrices, M1(z), M2(z) ∈ GL(m + 1, C[z]), generated by type I and type II Hermite-Padé polynomials respectively. Then we have M1(z)M2(z) ≡ Im+1, where Im+1 is the identity (m + 1) × (m + 1)matrix.The result is motivated by some novel applications of Hermite-Padé polynomials to the investigation of monodromy properties of Fuchsian systems of differential equations; see [12], [5], [10], [6], [8].Bibliography: [12] titles.

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“…. , n m ) ∈ N m+1 are normal for the HP polynomials associated with the tuple at the infinity point (see [9], [11]).…”

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confidence: 99%