I will recall the classical connection between the Padéapproximation problem for the Stieltjes transform of a measure and (nonhermitean) orthogonal polynomials.Then I will show how to extend this notion to the case where instead of "polynomials" in the Padé problem we use an appropriate subspace of meromorphic functions (and differentials) on an arbitrary Riemann surface of genus $g\geq 1$. I will then show how the theory bears its fruits when applied to a concrete example in genus $1$ (i.e. on a (real) elliptic curve), where all functions can be expressed in terms of classical Weierstrass and Jacobi functions.I will also indicate asymptotic results in this case expressing the strong asymptotic of the corresponding orthogonal “polynomials" (really, elliptic functions) and the weak limit of the counting measure of their zeroes. A connection with the potential theory of measures and Scurves will be hinted at, time permitting.
You are here
Padé approximants and orthogonality on Riemann surfaces
Research Group:
Speaker:
Marco Bertola
Institution:
Concordia University
Schedule:
Wednesday, June 14, 2023  16:00
Location:
A135
Abstract:
Openings
 Call of interest for positions in mathematics at SISSA
 Public Calls for Professors
 Temporary Professors/Researchers/Visiting Professors
 SISSA Mathematical Fellowships
 PostLauream Fellowships
 Research Training Fellowships
 Marie SklodowskaCurie Grants
 Open positions in MathLab
 Post Doctoral Fellowships
 PhD Scolarships
 SIS Fellowships
 Undergraduate Fellowships
 Postgraduate Fellowships
 MSc in Mathematics
 MSc in Data Science and Scientific Computing (DSSC)
 Professional Master Courses
 SISSA Mathematics Medals
Upcoming events

Pablo Alexei Gazca Orozco
Numerical computations and thermodynamically complete models for inelastic behaviour in solids
Monday, December 4, 2023  15:00

Paolo Piersanti
Variational Inequalities and their applications in elasticity and glaciology
Wednesday, December 6, 2023  16:00

Daniele Semola
Ricci Curvature, Fundamental Groups, and the Milnor Conjecture
Thursday, December 7, 2023  14:00 to 15:30

Jonathan Husson
TBA
Monday, December 11, 2023  16:00 to 17:00
Today's Lectures

09:00 to 11:00

11:00 to 13:00
Recent publications

G.P. Leonardi; G. Saracco,Rigidity and trace properties...

S. Salavatidezfouli; S. Hajisharifi; M. Girfoglio; G. Stabile; G. Rozza,Applicable Methodologies for t...

S. Carano,Relaxed area of $0$homogeneou...

G. Bellettini; S. Carano; R. Scala,Relaxed area of graphs of piec...