Polynomial sequences generated by infinite Hessenberg matrices

DOI10.1515/spma-2017-0002zbMath1360.15034OpenAlexW2580036407MaRDI QIDQ516662

Luis Verde-Star

Publication date: 15 March 2017

Published in: Special Matrices (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/spma-2017-0002

zbMATH Keywords

generating functionsrecurrence relationsmatrix similarityinfinite Hessenberg matricesinfinite Toeplitz matricesorthogonal polynomial sequencespolynomial sequences of interpolatory typeToeplitz companion matrices

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Canonical forms, reductions, classification (15A21) Toeplitz, Cauchy, and related matrices (15B05)

Related Items (7)

Recurrence relations and determinant forms for general polynomial sequences. Application to Genocchi polynomials ⋮ Infinite matrices in the theory of orthogonal polynomials ⋮ On a closed form for derangement numbers: an elementary proof ⋮ Linearization and connection coefficients of polynomial sequences: a matrix approach ⋮ Representation of doubly infinite matrices as non-commutative Laurent series ⋮ Polynomial sequences: elementary basic methods and application hints. A survey ⋮ Root location for the characteristic polynomial of a Fibonacci type sequence

Cites Work

• Infinite triangular matrices, \(q\)-Pascal matrices, and determinantal representations
• Elementary triangular matrices and inverses of \(k\)-Hessenberg and triangular matrices
• Introduction to large truncated Toeplitz matrices
• Characterization and construction of classical orthogonal polynomials using a matrix approach
• Is every matrix similar to a Toeplitz matrix?
• Toeplitz matrices, asymptotic linear algebra and functional analysis
• A note on the determinant of a Toeplitz-Hessenberg matrix
• Polynomial Sequences of Interpolatory Type

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