1998 — 2002 |
Suslov, Sergei |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Basic Fourier Series and Their Extensions @ Arizona State University
PRINCIPAL INVESTIGATOR: Sergei K. SUSLOV, PROPOSAL ID# DMS-9803443 PROPOSAL TITLE: Basic Fourier Series and Their Extensions ABSTRACT OF THE RESEARCH PROJECT The area of special functions, and q-series in particular, has seen significant advances in the last twenty years. One major event is the discovery of the Askey-Wilson polynomials. There are also a variety of recent problems in analysis, algebra, and combinatorics related to q-series. In the current project we plan to investigate basic Fourier series and their extensions. This is quite a new area of research in analysis. The Fourier and Fourier-Bessel series have a rich and deep theory. But only recently Ismail, Masson and Suslov have established a continuous orthogonality property for the basic Bessel functions and considered basic extension of the Fourier-Bessel series. Bustoz and Suslov have introduced basic Fourier series and established several facts about convergence of these series. Askey suggested that the "Bessel-type orthogonality" found by Ismail, Masson, and Suslov has a general character and can be extended to a larger class of basic hypergeometric series. Askey's conjecture has recently been proven by Suslov. In this project we propose to develop a theory of basic Fourier series and their higher extensions which is similar to the classical theory of Fourier and Fourier-Bessel series. This theory will include detailed study of properties of the new q-orthogonal functions, investigation of convergence of the corresponding series and related topics. This naturally includes certain computational problems: eigenvalues of the corresponding Sturm-Liouville problem can be found only numerically, investigation of convergence of these new series should be done. Explicit examples of basic Fourier series naturally lead to a new class of formulas never investigated before from the analytical and numerical viewpoint. The method of basic Fourier series can be applied to study solu tions of a q-heat equation and for some other basic versions of the equations of mathematical physics. The study of Fourier series has a long and distiguished history in mathematics. Historically, Fourier series were introduced in order to solve the heat equation, and since then these series have been frequently used in various applied problems. Much of modern real analysis including Lebesgue's fundamental theory of integration had its origin in some deep convergence questions in Fourier series. There is a great deal of interest these days in basic or q-extensions of Fourier series and their theory. In this project we intend to lay a sound foundation for this study. We introduce basic Fourier series, investigate their main properties, and consider some applications in mathematical physics.
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1 |
2000 — 2001 |
Bustoz, Joaquin Suslov, Sergei Ismail, Mourad |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
International Conference, Special Functions 2000: Perspective and Future Directions @ Arizona State University
This award is for the partial support of a conference in the field of Theory of Special Functions. The main emphasis of the conference will be on application of special functions in Number Theory, Quantum Groups, Mathematical Physics, Combinatorics and Computer Algebra. Such a multidisciplinary character of the conference makes it a significant event in the development of the field itself and its applications. The conference will be held in conjunction with the session of the Advanced Study Institute funded by NATO and will attract leading researchers in the field from many different countries and many young investigators. The conference will be jointly supported with the Division of International Programs.
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1 |
2003 — 2004 |
Suslov, Sergei |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
International Workshop On Special Functions, Orthogonal Polynomials, Quantum Groups and Related Topics @ Arizona State University
We propose to organize an International Workshop on Special Functions, Orthogonal Polynomials, Quantum Groups and Related Topics dedicated to Richard Askey on his 70th birthday. Date: 18--22 October 2003. Location: Hotel Hochwiesmuehle, Bexbach/Saarland, Germany. International Organizing Committee: Erik Koelink (Delft University of Technology, The Netherlands), Tom Koornwinder (KdV Institute, University of Amsterdam, The Netherlands), Jasper Stokman (KdV Institute, University of Amsterdam, The Netherlands), Andreas Ruffing (Munich University of Technology, Germany), Sergei Suslov (Arizona State University, United States). Local Organizing Committee: Andreas Ruffing (Chair), Kristine Ey, Clemens Lindemann (President of Saarpfalz District), Heinz Mueller (Mayor of the Town of Bexbach).
The area of special functions, in general and q-series in particular, has seen major and significant advances in the last thirty years. Recently the subject is being applied in different areas of mathematics and physics. The focus of the proposed workshop will be on the active research areas in special functions and their applications influenced by Richard Askey. This is especially important at a time, like the present, when the subject is being applied in many areas including quantum group, combinatorics, number theory, completely integrable systems, mathematical physics.
The main emphasis of the meeting will be the theory of special functions and their applications. A point of emphasis will be on recent developments in classical orthogonal polynomials, or Askey--Wilson polynomials and their special and/or limiting cases, biorthogonal rational functions, Leonard's pairs, integral transforms including q-Fourier transform and Askey--Wilson function transform, q-Fourier series, Askey--Wilson operators and their inverses, quantum groups and special functions, q-harmonic oscillators, and others.
The workshop will have truly international character; it will bring together all ``generations'' of Askey's mathematical family: from the world top leaders to young researchers and graduate students who are engaged in development of modern theory of special functions, q-series and their applications.
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1 |
2004 — 2005 |
Suslov, Sergei Castillo-Chavez, Carlos (co-PI) [⬀] |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
International School On Mathematical Modeling of Nonlinear Phenomena @ Arizona State University
This school will be held in Germany and Italy between September 28 and October 4 2004. It will bring five Arizona students majoring in mathematics and science (these are minority students) to work with fifteen German undergraduate students at this International School. The topics included will be ordinary and partial differential equations, Fourier analysis, mathematical biology and stochastic processes.
The US students are identified from Arizona State University having two major 'pipeline' programs for underrepresented minorities: the Mathematics-Science Honors Program and the Mathematical-Theoretical Biology Institute. These institutes have been active for several years, and train about 175 high school students and about 10 university students each year. These initiatives have already received national recognition.
It is expected that an opportunity for these students to interact with German students would increase the focus in mathematics and science in some underrepresented groups in the US. This program is being coordinated with an analogous program at the Munich Institute of Technology, which has been running several schools in the past four years.
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1 |
2014 |
Suslov, Sergei Castillo-Chavez, Carlos (co-PI) [⬀] Roudenko, Svetlana (co-PI) [⬀] Bohner, Martin (co-PI) [⬀] |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Conference On Partial Differential Equations (Copde2014), May 28 - June 1, 2014 @ Arizona State University
This award will support the participation of US students, early-career researchers, and members of underrepresented groups at the conference "International Conference on Partial Differential Equations", to be held in Novacella, Italy from May 28-June 1, 2014. The purpose of the conference is to report on recent important advances in the mathematical subject of partial differential equations. This is a subject that has considerable importance both for its intrinsic mathematical interest as well as for its centrality and uses in the modeling of physical phenomena and its applications in engineering and other important fields.
The conference is dedicated to the subject of partial differential equations. Topics will include stochastic partial differential equations, nonlinear Schrodinger and parabolic equations of paraxial optics, mathematical methods and computer simulation of tumor growth and therapy, mathematical physics, mathematical biology, and optimal control. Plenary and invited speakers will give presentations on the modern trends and results in partial differential equations in the morning, with a collection of contributed talks given in parallel sessions in the afternoon. There will be ample opportunity for the participants funded from this grant to present their work and to engage other experts in productive discussion.
Conference web site: https://math.la.asu.edu/~copde2014/
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1 |
2015 — 2016 |
Suslov, Sergei Roudenko, Svetlana [⬀] Bohner, Martin (co-PI) [⬀] |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
International Conference On Partial Differential Equations (Copde-2015) @ George Washington University
This award provides funding to help defray the expenses of U.S. participants in the "International Conference on Partial Differential Equations (COPDE-2015)" that will take place March 25-29, 2015, at the Technical University of Munich, in Munich, Germany.
This is the second in a series of conferences that each year will bring together a host of international authorities to explore a range of topics in the theory and applications of partial differential equations. Among the topics for discussion at COPDE-2015 are the following: stochastic partial differential equations; the Navier-Stokes equations; nonlinear Schrodinger equations and parabolic equations of paraxial optics; and mathematical methods and computer simulation of tumor growth and therapy. The conference program provides ample opportunity for graduate students, postdocs, and other young scientists to present their work.
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0.939 |