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\markboth{\sc \centerline{Proceedings of the IWOP'96} }{\sc \centerline{Proceedings of the IWOP'96} }


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\begin{center}
{\huge {\sc INTERNATIONAL WORKSHOP ON }

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{\bf ORTHOGONAL POLYNOMIALS }

\vspace*{.5cm}

{\bf IN MATHEMATICAL PHYSICS} }

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{\Large{\em In honour of Professor Andr\'e Ronveaux.}}

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{\large{\sc June 24-26, 1996.}}
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\vfill 

{\bf Edited by} \\

{\large{\sc  M. Alfaro, R. \'Alvarez-Nodarse, G. L\'opez Lagomasino, and F. Marcell\'an}}
 
\newpage 

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\noindent{\bf Editors} \\

\noindent Manuel Alfaro\\
Departamento de Matem\'aticas. Universidad de Zaragoza. Spain.\\

\noindent Renato \'Alvarez-Nodarse\\
Departamento de Matem\'aticas. Universidad Carlos III de Madrid. Spain.\\

\noindent Guillermo L\'opez Lagomasino \\
Departamento de Matem\'aticas. Universidad Carlos III de Madrid. Spain y 
Departamento de Teor\'{\i}a de Funciones. Universidad de la Habana. Cuba.\\


\noindent Francisco Marcell\'an\\
Departamento de Matem\'aticas. Universidad Carlos III de Madrid. Spain.\\

\vskip 3cm 
\noindent {\bf AMS (MSC 1991) Subject Classification}: Primary 42C05, 33D45,
33C45, 33C80, 33C90




\vskip 3cm 
\vfill
\noindent\copyright 1997 by M. Alfaro, R. \'Alvarez-Nodarse, G. L\'opez Lagomasino,  and F. Marcell\'an\\
\noindent {\bf ISBN:84-605-6154-2}    \\
\noindent {\bf Dep\'osito Legal:M-9779-1997}  \\
\noindent {\bf Presentaci\'on y enmaquetaci\'on:}   R. \'Alvarez-Nodarse\\
\noindent {\bf Dise\nc o de la portada:} R. \'Alvarez-Nodarse\\
\noindent Este documento ha sido escrito y compilado con \LaTeX2e  \,\, y \TeX \,\,
Version 3.14159 (C version 6.1)


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A three-day ``International Workshop   on Orthogonal Polynomials in 
Mathematical Physics'' was hosted by  Departamento de Matem\'aticas, 
Universidad Carlos III de Madrid, which took place during the past June 24-26,
1996. \\

A total of 74 participants engaged in friendly discussions and a pleasant 
atmosphere  accompanied the meeting. Thirteen spanish institutions were 
represented by 53 people and another thirteen foreigner institutions by the 
rest.   Each of the five invited speakers gave two one-hour lectures
whose title were
  
\begin{itemize}
 \item  Natig Atakishiyev (Instituto de Investigaciones en Matem\'aticas Aplicadas y en 
 Sistemas. Universidad  Nacional Aut\'{o}noma de M\'{e}xico. Cuernavaca. M\'{e}xico.)
 {\em Difference Equations and Some of their Solutions. Ramanujan-type Continuous Measures 
 for Classical q-Polynomials.}
 
 \item  Alexander I. Aptekarev (Keldysh Institut Russian Academy of Sciences, Moscow.) {\em Toda-type 
 Dynamics for the Coefficients of Recurrence Relations.}

 \item  Jes\'us S. Dehesa (Departamento de F\'{\i}sica Moderna. Universidad  de Granada, Spain.)
 {\em Information Theory, Quantum Entropy and Orthogonal Polynomials.}

 \item  Hendrik Koelink (University  of Amsterdam. The Netherlands.) {\em  Addition Formulas for 
 $q$-Special Functions. Hecke algebras and $q$-Krawtchouk polynomials.}

 \item  Yuri F. Smirnov  (Instituto de F\'{\i}sica, Universidad  Nacional Aut\'{o}noma de M\'{e}xico. 
 M\'{e}xico.) {\em Orthogonal polynomials of a Discrete Variable 
 and Quantum algebras $SU_q(2)$  and  $SU_q(1,1)$.  Hidden  $sl(2)$ Algebra of the Finite Difference Equations.}

\end{itemize}
 
The sessions were completed by thirteen half-hour communications. These short 
communications were delivered by


\begin{itemize}
   \item Jorge Arves\'u: {\em The Laguerre polynomials in a relativistic quantum-statistical model.}
   \item Antonio Dur\'an: {\em On orthogonal matrix polynomials.}
   \item Federico Finkel: {\em Quasi Exactly Solvable Potentials on the Line and Orthogonal 
         Polynomials.}
   \item Wolfgang Grawronski: {\em On the Zeros of Classical Orthogonal Polynomials with Large 
         Complex Parameters.}
   \item Lucas J\'odar: {\em A Matrix Formula for the Generating Function  of the Product of Hermite 
         Matrix Polynomials.}
   \item Roelof Koekoek: {\em  Recent Developments in the Research of  Differential Operators  for 
         Generalized (Sobolev) Orthogonal Polynomials.} 
   \item Pierpaolo Natalini: {\em Some New Sets of Relativistic Orthogonal Polynomials.}
   \item Ram\'on Orive: {\em Rational Approximation to Certain  Functions with Branch Points.}
   \item Franz Peherstorfer: {\em  Periodic and quasiperiodic Toda lattices.}
   \item Jos\'e Carlos Petronilho: {\em On Some Polynomial Modifications of Measures. Applications.}
   \item Andr\'e Ronveaux: {\em Orthogonal Polynomials: Connection and Linearization  Coefficients.}
   \item Jorge S\'anchez-Ruiz: {\em Position and momentum information entropies of the harmonic 
         oscillator and logarithmic potential of Hermite polynomials.}
   \item Franciszek Szafraniec: {\em  Orthogonal polynomials in building  models  of  the  quantum  
         harmonic oscillator. }
   \item Aldo Tagliani: {\em Entropy-convergence, Instability in Stieltjes and Ham\-bur\-ger Moment 
         Problems.}
   \end{itemize}  

The organizing Committee was constituted by  Manuel Alfaro (Universidad  de Zaragoza), 
Renato \'Alvarez-Nodarse (Secretary) (Universidad  Carlos III de Madrid), Antonio Garc\'{\i}a 
Garc\'{\i}a (Universidad  Carlos III de Madrid), Guillermo  
L\'opez Lagomasino (Universidad  Carlos III de Madrid and Universidad de la Habana) 
and  Francisco Marcell\'an (Chairman) (Universidad  Carlos III de Madrid). \\
  
All speakers were kindly invited to submit written versions of their talks for 
the proceedings of the meeting which we present here.
The Workshop was dedicated in honour of Professor Andr\'e Ronveaux on the occasion of his 
retirement from Facult\'es Universitaires Notre Dame de la Paix (Namur, Belgium)  and his fruitful 
mathematical activities.\\


{\bf The calendar of the sessions was}\\

\begin{center}
\begin{tabular}{| c ||c |c| c|}
\hline 
   & Monday & Tuesday & Wednesday \\
\hline
\hline
 9:30 & Smirnov & Aptekarev  & Dehesa  \\
\hline
 10:30 & Break & Break & Break \\
\hline
 10:45 & Koelink    &  Smirnov   &     Koelink   \\
\hline
 11:45 & Break & Break & Break \\
\hline
 12:15 &  Ronveaux & Koekoek   &  Tagliani \\
\hline
 12:45 & Natalini & Gawronski &   S\'anchez-Ruiz \\
\hline
 13:15 & Szafraniec & Peherstorfer     & Finkel \\
\hline  
 14:00  & Lunch & Lunch & Lunch  \\
\hline
15:30 & Arves\'u & Orive  & Petronilho \\
\hline
16:00 &  Atakishiyev  &  Dehesa   &  Duran / Jodar  \\
\hline
 17:00 & Break & Break &  Break  \\
\hline
 17.15 &  Aptekarev   &  Atakishiyev   &  Open Problems  \\
\hline
\end{tabular}
\end{center}

\vspace*{.3cm}

The workshop was sponsored by Universidad Carlos III de Madrid, INTAS, Consejer\'\i a de Educaci\'on 
y Cultura (Comunidad Aut\'onoma de Madrid), Direcci\'on General de Ense\nc anza Superior 
(Ministerio de Educaci\'on y Cultura of Spain). Our acknowledgement to all these institutions
for their financial support. 

\vspace*{3cm}


{\hfill  The organizing Committee} 




\vskip 1cm
\newpage

 \centerline{ \Large {\bf Table of Contents}}

\vspace{24pt}

\noindent 1. {\small\em{ON SOME POLYNOMIAL MAPPINGS FOR MEASURES. APPLICATIONS}} \\
\esp {R. \'Alvarez-Nodarse, F. Marcell\'an, and J. Petronilho } \hfill 1

\vspace{8pt}

\noindent 2. {\small\em{THE LAGUERRE POLYNOMIALS IN A RELATIVISTIC 
QUANTUM-STATISTICAL MODEL }} \\
\esp {J. Arves\'u } \hfill 23

\vspace{8pt}

\noindent 3. {\small\em{CONTINUOUS SOLUTIONS OF DIFFERENCE EQUATIONS AND THEIR ORTHOGONALITY} } \\
\esp {N. M. Atakishiyev } \hfill 37


%%\vspace{8pt}

%%\noindent 4. {\small\em{INFORMATION THEORY, QUANTUM ENTROPY AND ORTHOGONAL POLYNOMIALS } } \\
%%\esp {J. S. Dehesa } \hfill 1


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\noindent 4. {\small\em{ON ORTHOGONAL MATRIX POLYNOMIALS} } \\
\esp {A. Duran} \hfill 63


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\noindent 5. {\small\em{ORTHOGONAL POLYNOMIALS AND QUASY-EXACTLY SOLVABLE POTENTIALS ON THE LINE  } } \\
\esp {F. Finkel, A. Gonz\'alez-L\'opez, and M.A. Rodr\'\i guez } \hfill 73


\vspace{8pt}

\noindent 6. {\small\em{ENTROPY-CONVERGENCE, INSTABILITY IN STIELTJES
AND HAMBURGER MOMENT PROBLEMS}} \\
\esp { M. Frontini and A. Tagliani} \hfill 81


\vspace{8pt}

\noindent 7. {\small\em{SOME NEW MATRIX FORMULAS RELATED TO HERMITE MATRIX POLYNOMIALS   } } \\
\esp {L. J\'odar and E. Defez } \hfill 93


\vspace{8pt}

\noindent 8. {\small\em{FINDING DIFFERENTIAL EQUATIONS FOR SYMMETRIC GENERALIZED
 ULTRASPHERICAL POLYNOMIALS BY USING INVERSION METHODS  } } \\
\esp {J.~Koekoek and R.~Koekoek } \hfill 103


\vspace{8pt}

\noindent 9. {\small\em{CONVOLUTION AND ADDITION THEOREMS  FOR $q$-ORTHOGONAL POLYNOMIALS  } } \\
\esp {E.~Koelink} \hfill 113


\vspace{8pt}



\noindent 10. {\small\em{A CLASS OF JACOBI POLYNOMIALS ORTHOGONAL WITH RESPECT TO VARYING 
WEIGHTS}} \\
\esp { M. X. He,   P. Natalini,   and   P.E. Ricci} \hfill 123


\vspace{8pt}

\noindent 11. {\small\em{ ORTHOGONAL POLYNOMIALS:  CONNECTION AND LINEARIZATION COEFFICIENTS  } } \\
\esp {A. Ronveaux } \hfill 131


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\noindent 12. {\small\em{POSITION AND MOMENTUM INFORMATION ENTROPIES OF THE
HARMONIC OSCILLATOR AND LOGARITHMIC POTENTIAL OF HERMITE POLYNOMIALS}} \\
\esp { J. S\'anchez-Ruiz } \hfill 143


\vspace{8pt}

\noindent 13. {\small\em{ON FACTORIZATION AND ALGEBRAIZATION OF  DIFFERENCE EQUATIONS 
OF HYPERGEOMETRIC TYPE  } } \\
\esp {Yu. F. Smirnov} \hfill 153


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\noindent  {\small\em{LIST OF PARTICIPANTS} } \hfill 163 
%%% \\ \esp { } \hfill 163


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