# Orthogonal polynomials

People: |
Domenico Castrigiano |

Frank Hofmaier |

*orthonormalizing measure*can be obtained from the spectral measure of a normal extension of a Hessenberg operator, namely multiplication by the independent variable in

**C**[Z], in some abstract Hilbert space. Therefore, the theory of orthogonal polynomials is closely related to spectral theory of subnormal Hessenberg operators.

## Publications

- D.P.L. Castrigiano, Orthogonal polynomials and rigged Hilbert space,
*J. Functional Analysis*65: 309 - 313, 1986 - D.P.L. Castrigiano, W. Klopfer, Orthonormal bases of polynomials in one complex variable,
*Analysis Mathematica*29: 7 - 14, 2003 - F. Hofmaier, Orthogonal Polynomials: Interaction between Orthogonality in L
^{2}-spaces and Orthogonality in Reproducing Kernel Spaces, Dissertation, TU München, 2007, http://mediatum2.ub.tum.de/node?id=609229 - D. Castrigiano, F. Hofmaier: Bounded point evaluations for orthogonal polynomials,
*Advances and Applications in Mathematical Sciences***10**(4) (2011), 373-392