Geodesic
Three cases of normality of Hessenberg's matrix related with atomic complex distributions
Electronic transactions on numerical analysis, Tome 19 (2005), pp. 105-112.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this work we prove that Hessenberg's infinite matrix, associated with an hermitian OPS that generalizes the Jacobi matrix, is normal under the assumption that the OPS is generated from a discrete infinite bounded distribution of non-aligned points in the complex plane with some geometrical restrictions. This matrix is also normal if we consider a real bounded distribution with a finite amount of atomic complex points. In this case we still have normality with infinite points, but an additional condition is required. Some other interesting properties of that matrix are obtained.
Classification : 33C45
Keywords: orthogonal polynomials, hessenberg`s matrix, normal operator 
@article{ETNA_2005__19__a1,
     author = {Tomeo, Venancio and Torrano, Emilio},
     title = {Three cases of normality of {Hessenberg's} matrix related with atomic complex distributions},
     journal = {Electronic transactions on numerical analysis},
     pages = {105--112},
     publisher = {mathdoc},
     volume = {19},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2005__19__a1/}
}
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Tomeo, Venancio; Torrano, Emilio. Three cases of normality of Hessenberg's matrix related with atomic complex distributions. Electronic transactions on numerical analysis, Tome 19 (2005), pp. 105-112. http://geodesic.mathdoc.fr/item/ETNA_2005__19__a1/