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July 25-29,2011
Conference on Blaschke Products and their Applications
Hosted by the Fields Institute, held at the University of
Toronto
Bahen Building(BA1200)map
Organizers: Javad
Mashreghi (Laval, Canada),
Emmanuel Fricain (Lyon I, France
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OVERVIEW
Infinite Blaschke products were introduced by Blaschke in 1915.
However, finite Blaschke products, as a subclass of rational functions,
has existed long before without being specifically addressed as
finite Blaschke products. In 1929, R. Nevanlinna introduced the
class of bounded analytic functions with almost everywhere unimodular
boundary values. Then the term inner function was coined much later
by A. Beurling in his seminal study of the invariant subspaces of
the shift operator.
The first extensive study of the properties of inner functions
was made by Frostman, Seidel and F. Riesz. The Riesz technique in
extracting the zeros of a function in a Hardy space is considered
as the first step of the full canonical factorization of such elements.
The disposition of zeros of an inner function is intimately connected
with the existence of radial limits of the inner function and its
derivatives.
For almost a century Blaschke products have been studied and exploited
by mathematicians. Their boundary behaviour, the asymptotic growth
of various integral means of Blaschke products and their derivatives,
their applications in several branches of mathematics in particular
as solutions to extremal problems, their membership in different
function spaces and their dynamics are examples from a long list
of active research domains in which they show their face.
In this conference, prominent mathematicians from around the world
will gather to talk about these beautiful creatures and their application
in other domains.
Monday, July
25 (Bahen Centre Room 1200) map
Chair: William Ross (AM), Artur Nicolau (PM) |
| 8:00-8:20 |
On-site Registration & Morning
Coffee |
| 8:20-8:30 |
Welcome & Introduction |
| 8:30-9:30 |
Pamela Gorkin (Bucknell University)
To get (or not to get) uniform approximation by interpolating
Blaschke products |
| 9:30-10:30 |
Laurent Baratchart (INRIA)
Rational approximation and Morse theory |
| 10:30-10:50 |
Coffee Break |
| 10:50-11:50 |
Joseph Cima (University of North Carolina)
A survey of recent results on TTO's |
| 11:50-14:00 |
Lunch Break |
| 14:00-15:00 |
Ulrich Daepp (Bucknell University)
Geometric Properties of Finite Blaschke Products |
| 15:00-16:00 |
Eugene Shargorodsky (King's College)
Applications of Blaschke products to the spectral theory
of Toeplitz operators |
| 16:00-16:20 |
Coffee Break |
| 16:20-17:20 |
Line Baribeau (Laval University)
Hyperbolic divided differences |
| 17:20-18:20 |
Reception (Fields Institute
Atrium, 222 College St.) Cash Bar |
Tuesday,
July 26 (Bahen Centre Room 1200)
map
Chair: Laurent Baratchart (AM), Eugene Shargorodsky (PM) |
| 8:00-8:30 |
Morning Coffee |
| 8:30-9:30 |
William Ross (University of Richmond)
Boundary values of functions in the range of a truncated
Toeplitz operator |
| 9:30-10:30 |
Jie Xiao (Memorial University of Newfoundland)
Isoperimetry for Green's Function and Torsional Rigidity
over Riemannian Surfaces |
| 10:30-10:50 |
Coffee Break |
| 10:50-11:50 |
Artur Nicolau (Universitat Autònoma
de Barcelona)
Paths of Inner Functions |
| 11:50-14:00 |
Lunch Break |
| 14:00-15:00 |
Daniela Kraus (University of Wuerzburg)
Critical sets of bounded analytic functions, zero sets of
Bergman spaces and nonpositive curvature |
| 15:00-16:00 |
Oliver Roth (University of Würzburg)
Properties of maximal conformal metrics and their developing
maps |
| 16:00-16:20 |
Coffee Break |
| 16:20-17:20 |
Margit Pap (University of Vienna)
Application of the Blaschke products in Harmonic Analysis
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Wednesday,
July 27 (Bahen Centre Room 1200)
map
Chair: Oliver Roth (AM), Richard Fournier (PM) |
| 8:00-8:30 |
Morning Coffee |
| 8:30-9:30 |
Janne Heittokangas (University of Joensuu)
On Blaschke-Oscillatory Differential Equations |
| 9:30-10:30 |
Richard Fournier (Université de
Montréal)
On two problems involving finite Blaschke products |
| 10:30-10:50 |
Coffee Break |
| 10:50-11:50 |
Wlodzimierz Zwonek (Jagiellonian University)
Pluripolar extension of Blaschke products |
| 11:50-14:00 |
Lunch Break |
| 14:00-15:00 |
Sergei Favorov (Kharkov Naeional University)
Blaschke-type conditions for analytic functions in the unit
circle and critical points of Blaschke products |
| 15:00-16:00 |
Qazi Ibadur Rahman (Université
de Montréal)
Local behaviour of entire functions of exponential type |
| 16:00-16:20 |
Coffee Break |
| 16:20-16:50 |
Mohammed A. Qazi (Tuskegee University)
An inequality for functions belonging to the Paley-Wiener
space |
| 16:50-17:20 |
Driss Drissi (Kuwait University)
Invariant subspaces for some sequences operator algebras |
| 17:20-17:50 |
Jamal Benbourenane (Abu Dhabi University)
An Application of Blaschke Products to Algebraic Differential
Equations |
Thursday,
July 28 (Bahen Centre Room 1200)
map
Chair: Ulrich Daepp (AM), Joseph Cima (PM) |
| 8:00-8:30 |
Morning Coffee |
| 8:30-9:30 |
Dragan Vukotic (Universidad Autónoma
de Madrid & ICMAT)
Integrability of the derivatives of Blaschke products and
applications |
| 9:30-10:30 |
Christer Glader (Åbo Akademi University)
Nonlinear Riemann-Hilbert Problems with Circular Target Curves
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| 10:30-10:50 |
Coffee Break |
| 10:50-11:50 |
Igor Chyzhykov (Lviv National University)
Growth, zero distribution and factorization of analytic functions
of moderate growth in the unit disc |
| 11:50-14:00 |
Lunch Break |
| 14:00-15:00 |
Vasiliy Prokhorov (University of South
Alabama)
On Approximation of Analytic Functions |
| 15:00-15:30 |
Patrick Tuen-Wai Ng (University of Hong
Kong)
Chebyshev-Blaschke products |
| 15:30-16:00 |
Gunter Semmler (Fakultät für
Mathematik und Informatik)
Interpolation with Blaschke products and phase portraits |
| 16:00-16:20 |
Coffee Break |
| 16:20-16:50 |
Andre Boivin (University of Western Ontario)
A Bi-orthogonal Expansion in the Space L2(R+) |
| 16:50-17:20 |
Stephane Charpentier (Universite Paris
Sud)
Composition operators on Hardy-Orlicz and Bergman-Orlicz
spaces on the ball
|
| 17:20-17:50 |
Helene Bommier (University of Provence)
Bergman type projections and operators on generalized Fock
spaces |
Friday, July
29 (Bahen Centre Room 1200) map
Chair: Pamela Gorkin (AM) |
| 8:00-8:30 |
Morning Coffee |
| 8:30-9:30 |
Timothy McNicholl (Lamar University)
Blaschke products and inner functions from the viewpoint
of the theory of computation |
| 9:30-10:30 |
Armen Edigarian (Jagiellonian University)
Blaschke products in pluripotential theory |
| 10:30-10:50 |
Coffee Break |
| 10:50-11:50 |
Oleg Ivrii (Harvard University)
On the Weil-Petersson metric on the space of Blaschke products |
| 11:50-12:00 |
Closing Remarks |
Baratchart, Laurent -- INRIA
Baribeau, Line -- Laval University
Benbourenane, Jamal --Abu Dhabi University
Chyzhykov, Igor -- Lviv National University
Cima, Joseph -- University of North Carolina
Daepp, Ulrich -- Bucknell University
Edigarian, Armen-- Jagiellonian University
Fournier, Richard -- Université de Montréal
Glader, Christer -- Åbo Akademi University
Gorkin, Pamela -- Bucknell University
Heittokangas, Janne -- University of Joensuu
Kraus, Daniela -- University of Wuerzburg
McNicholl, Timothy -- Lamar University
Nicolau, Artur -- Universitat Autònoma de Barcelona
Pap, Margit -- University of Vienna
Patrick, Tuen-wai Ng --The University of Hong Kong
Prokhorov, Vasiliy -- University of South Alabama
Rahman, Qazi Ibadur -- Université de Montréal
Ross, William -- University of Richmond
Roth, Oliver -- University of Würzburg
Semmler, Gunter -- Fakultät für Mathematik und Informatik
Shargorodsky, Eugene -- King's College
Vukotic, Dragan -- Universidad Autónoma de Madrid
& ICMAT
Xiao, Jie -- Memorial University of Newfoundland
Zwonek, Wlodzimierz -- Jagiellonian University
Confirmed Participants as of July 18,
2011
| Full Name |
University Name |
| Baratchart, Laurent |
INRIA Sophia Antipolis - Méditerranée |
| Baribeau, Line |
Université Laval |
| Benbourenane, Jamal |
Abu Dhabi University |
| Boivin, André |
University of Western Ontario |
| Bommier, Hélène |
Université de Provence |
| Charpentier, Stéphane |
Université Paris-Sud |
| Chyzhykov, Igor |
Lviv National University |
| Cima, Joseph |
University of North Carolina |
| Daepp, Ulrich |
Bucknell University |
| Drissi, Driss |
Kuwait University |
| Edigarian, Armen |
Jagiellonian University |
| Favorov, Sergii |
Kharkov National University |
| Fournier, Richard |
Université de Montréal |
| Fricain, Emmanuel |
Université Claude Bernard Lyon 1 |
| Glader, Christer |
Åbo Akademi University |
| Gorkin, Pamela |
Bucknell University |
| Heittokangas, Janne |
University of Joensuu |
| Ivrii, Oleg |
Harvard University |
| Kraus, Daniela |
University of Wuerzburg |
| Li, Daniel |
Université d'Artois |
| Mashreghi, Javad |
Université Laval |
| McNicholl, Timothy |
Lamar University |
| Ng, Tuen Wai |
The University of Hong Kong |
| Nicolau, Artur |
Universitat Autonoma de Barcelona |
| Pap, Margit |
University of Pécs |
| Pozzi, Elodie |
Université Lyon I |
| Prokhorov, Vasiliy |
University of South Alabama |
| Qazi, Mohammed |
Tuskegee University |
| Rahman, Qazi Ibadur |
Université de Montréal |
| Ross, William |
University of Richmond |
| Roth, Oliver |
University of Würzburg |
| Schippers, Eric |
University of Manitoba |
| Semmler, Gunter |
Technische Universität Bergakademie Freiberg |
| Shargorodsky, Eugene |
King's College London |
| Vukotic, Dragan |
Universidad Autónoma de Madrid & ICMAT |
| Xiao, Jie |
Memorial University of Newfoundland |
| Zorboska, Nina |
University of Manitoba |
| Zwonek, Wlodzimierz |
Jagiellonian University |
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