Green functions and polynomials  Page description

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Details of project

 
Identifier
49448
Type K
Principal investigator Totik, Vilmos
Title in Hungarian Green függvények és polinomok
Title in English Green functions and polynomials
Panel Mathematics and Computing Science
Department or equivalent Bolyai Institute (University of Szeged)
Participants Nagy, Béla
Toókos, Ferenc
Varjú, Péter Pál
Starting date 2005-01-01
Closing date 2009-12-31
Funding (in million HUF) 6.349
FTE (full time equivalent) 5.92
state closed project





 

Final report

 
Results in Hungarian
A támogatott kutatás a "potenciálelmélet és annak approximációelméleti alkalmazásai" területen történt. Elsősorban polinomok aszimptotikus tulajdonságait vizsgáltuk, amelyekkel kapcsolatban természetes módon lépnek fel logaritmikus potenciálok mint a zérushelyek határeloszlása. Másik, intenzíven vizsgált rokon terület az ortogonális polinomok elmélete. Jelentős előrelépés történt tübb kérdéskörben, így a változó súllyal vett polinom-approximációval, homogén polinomokkal való approximációval illetve az ún. univerzalitási hipotézissel kapcsolatban. Pályázati támogatással 16 publikáció (közöttük két könyv) született.
Results in English
The supported research focused on the applications of potential theory in approximation. Our primary goal was to investigate asymptotic properties of polynomials, where logarithmic potentials emerge as limiting zero distributions. Other related and intensively studied area was the theory of orthogonal polynomials. Considerable advancement was made in several fields, among others in weighted approximation by polynomials with varying weights; in approximation by homogeneous polynomials; and in connection with the so called universality hypothesis. With the support of OTKA altogether 17 works (among them two books) have been published.
Full text http://real.mtak.hu/1976/
Decision
Yes





 

List of publications

 
Vilmos Totik: Orthogonal polynomials, Surveys in Approximation Theory, 2005
Leonid Golinskii and Vilmos Totik: Orthogonal Polynomials from Jacobi to Simon, Proc. Sump. in Pure and Applied Math., AMS, 2007
Péter Komjáth and Vilmos Totik: Ultrafilters, American Mathematical Monthly, 2008
Hatvani L., Toókos F. and Tusnády G.: A mutation-selection-recombination model in population genetics, Dynamical Systems and Applications, 2009
Vilmos Totik: Equilibrium measures and polynomials, Proceedings of the 4th European Congress of Mathematicians, 2005
Bela Nagy: Bernstein inequality in L^a norms, Analysis Math., 2009
Peter Komjáth and Vilmos Totik: Problems and Theorems in Classical Set Theory, Problem books in Mathematics, Springer Verlag, 2006
Peter Varju: Approximation by homogeneous polynomials, Constructive Approximation, 2006
Vilmos Totik: Metric Properties of Harmonic Measures, Memoirs of the American Math. Soc., 2006
Peter Varjú: Approximation by homogeneous polynomials, Constructive Approximation, 2007
Vilmos Totik and Peter Varjú: Smooth equilibrium measures and approximation, Advances in Mathematics, 2007
Vilmos Totik and Peter Varjú: Polynomials with prescribed zeros and small norm, Acta Sci. Math., 2007
Balint Farkas and Bela Nagy: Transfinite diameter, Chebyshev constant and energy on locally compact spaces, Potential Analysis, 2008
Vilmos Totik: Universality and fine zero spacing on general sets, Arkiv för Mathematik, 2008
Vilmos Totik: Chebyshev constants and the inheritance problem, Journal of Approximation Theory, 2008
Jordaan K. and F. Toókos: Convexity of the zeros of some orthogonal polynomials, J. Comp. Appl. Math., 2009




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