Dear Colleagues,

As you know the last June 1996 held in Leganés the third edition
of the Worshop on Orthogonal Polynomials organized by Universidad Carlos III.
The aim of these Workshops was that a reduced
number of invited specialist discuss and review various recent works of the Theory of *Orthogonal Polynomials* and its applications. The first issue
(1992) was devoted to Sobolev Polynomials, the next (1994) to Polynomials on
the Unit Circle and the last one (1996) to Mathematical Physics. Here we
will report about the last one.

The IWOP'96 took place in the main building of the
Escuela Politécnica Superior. Universidad Carlos III de Madrid. Leganés, Madrid, from June 24-26, 1996.

The topics considered were

- q-Polynomials and related topics.
- Entropy of polynomials and related physical problems.
- Difference equations and their solutions.
- Finite difference equations and the (quasi) exact solvability concept.
- Toda lattices and Orthogonal Polynomials.
- Orthogonal Polynomials in Mathematical Physics.

- N. Atakishiev (Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas. Univ. Nacional Autónoma de México. Cuernavaca. México.)
- Jesus S. Dehesa (Departamento de Física Moderna. Univ. de Granada, Spain.)
- Yuri F. Smirnov (Instituto de Física, Univ. Nacional Autónoma de México. México.)
- H.T. Koelink (Univ. of Amsterdam. The Netherlands.)
- A. Aptekarev (Keldysh Institut Russian Academy of Sciences, Moscow.)

The Organizing Committee was

- M. Alfaro (Univ. de Zaragoza) ,
- R. Álvarez-Nodarse (Secretary) (Univ. Carlos III),
- A.G.García (Univ. Carlos III),
- G.López Lagomasino (Univ. Carlos III) and
- F. Marcellán (Chairman) (Univ. Carlos III)

The Scientific Committee was

- J. S. Dehesa (Univ. de Granada.)
- A. Aptekarev (Keldysh Institut Russian Academy of Sciences.)
- W. Van Assche (Katholieke Universiteit Leuven)
- G.López Lagomasino (Univ. Carlos III) and
- F. Marcellán (Univ. Carlos III)

Time | Monday | Tuesday | Wednesday |
---|---|---|---|

9:30 | Smirnov | Aptekarev | Dehesa |

10:30 | Break | Break | Break |

10:45 | Koelink | Smirnov | Koelink |

11:45 | Break | Break | Break |

12:15 | Ronveaux | Jodar | Tagliani |

12:45 | Natalini | Gawronski | Sánchez-Ruiz |

13:15 | Szafraniec | Peherstorfer | Finkel |

13:45 | Lunch | Lunch | Lunch |

15:40 | Arvesú | Orive | Petronilho |

16:00 | Atakishiev | Dehesa | Duran / Koekoek |

17:00 | Break | Break | Break |

17.15 | Aptekarev | Atakishiev | Open Problems |

- A. Aptekarev.
*Toda-type Dynamics for the Coefficients of Recurrence Relations. (2 hours)* - N. Atakishiev:
*Difference Equations and Some of their Solutions (1 hour). Ramanujan-type Continuous Measures for Classical q-Polynomials (1 hour).* - Jesus S. Dehesa:
*Information Theory, Quantum Entropy and Orthogonal Polynomials (2 hours).* - H.T. Koelink:
*Addition Formulas for q -Special Functions (1 hour). Hecke algebras and q-Krawtchouk polynomials (1 hour).* - Yuri F. Smirnov:
*Orthogonal polynomials of a Discrete Variables and Quantum algebras SUq(2) and SUq(1,1) (1 hour). Hidden sl(2) Algebra of the Finite Difference Equations (1 hour).*

- J. Arvesú:
*The classical Laguerre polynomials in a relativistic quantum-statistical model.* - A. Duran:
*On orthogonal matrix polynomials* - F. Finkel:
*Quasi Exactly Solvable Potentials on the Line and Orthogonal Polynomials.* - W. Grawronski
*On the Zeros of Classical Orthogonal Polynomials with Large Complex Parameters.* - L. Jódar:
*A Matrix Formula for the Generating Function of the Product of Hermite Matrix Polynomials.* - R. Koekoek:
*Recent Developments in the Research of Differential Operators for Generalized (Sobolev) Orthogonal Polynomials.* - P. Natalini:
*Some New Sets of Relativistic Orthogonal Polynomials.* - R. Orive:
*Rational Approximation to Certain Functions with Branch Points.* - F. Peherstorfer:
*Periodic and quasiperiodic Toda lattices.* - J. Petronilho:
*On Some Polynomial Modifications of Measures. Applications.* - A. Ronveaux:
*Orthogonal Polynomials: Connection and Linearization Coefficients.* - Jorge Sánchez-Ruiz:
*Position and momentum information entropies of the harmonic oscillator and logarithmic potential of Hermite polynomials.* - F. Szafraniec:
*Orthogonal polynomials in building models of the quantum harmonic oscillator.* - A. Tagliani:
*Entropy-convergence, Instability in Stieltjes and Hamburger Moment Problems.*

The workshop was sponsored by Universidad Carlos III de Madrid, INTAS, Consejería de Educación y Cultura (Comunidad Autónoma de Madrid), Dirección General de Enseñanza Superior (Ministerio de Educación y Cultura of Spain). Our acknowledgement to all these institutions for their financial support.

We have prepared an Special Monography with the Proceedings of the Workshop. You can find here the LaTeX/TeX or Postscript files.

Maintained by Renato Álvarez-Nodarse: E-Mail: ran@us.es