Analysis Seminar
- Fall 2004 -

Time: 2:40-3:30 Wednesday, Room: PSA 113
Contact:  Svetlana Roudenko svetlana [at] math.asu.edu

DATE
SPEAKER TOPIC/ABSTRACT
October 27, Wednesday   Organizational Meeting
  
 November 3, Wednesday
  Sergei Suslov, ASU
   "Asymptotics of Zeros of Basic Sine and Cosine Functions"
  ABSTRACT: We derive improved asymptotics of the basic sine  and cosine functions by a method using the Lagrange inversion formula.
November 10,
Wednesday
  no meeting
  
November 17,
Wednesday
 John McDonald, ASU
  "Phase Retrieval Problems"
  ABSTRACT: We discuss the problem of determining a "signal", i.e. function on the line from its magnitude.  Some new results on this problem are obtained using entire functions and Hardy  spaces on the upper half plane.
November 18,
Thursday
Michael Frazier, Michigan State University
(Colloquim, LSE 106, 3:40-4:30pm)
 "Why Mathematicians and some Non-Mathematicians care about Wavelets"
ABSTRACT: Wavelets were developed in the mid 1980s, to a large extent by harmonic  analysts.  Since then, wavelets have found  dramatic applications in many areas, such as image compression, medicine, and automotive engineering.  I will start by describing the mathematics of wavelets from the standpoint of harmonic analysis. Later in the talk, I will give a few examples of  wavelet applications, and indicate the main reasons for the popularity of wavelets in engineering and science. 
November 24,
Wednesday 		 no meeting; Thanksgiving break
  
December 1,
Wednesday		   shifted to Thursday, see below  
December 2,
Thursday

Krishnaswami Alladi, University of Florida
(Colloquim, PSA 306, 3:40-4:30pm)

 		   Rogers-Ramanujan type partition theorems and their analytic representations
 
ABSTRACT: A Rogers-Ramanujan (R-R) type partition identity connects 
partitions defined by difference conditions with partitions governed by 
congruence conditions. The name stems from the celebrated R-R identities 
which connect partitions into parts differing by at least 2 with partitions 
into certain residue classes mod 5. Ramanujan viewed these analytically in 
terms of a continued fraction and studied modular transformations of the 
fraction. In this talk we will discuss a hierarchy of R-R type theorems that 
can be understood by means of certain analytic key identities. The interplay 
between the analytic and combinatorial approaches leads to new perspectives 
in the theory of partitions and q-series. Some applications include new 
proofs of Jacobi's triple product identity for theta functions and some 
congruences modulo powers of 2 for certain partition functions. The talk will 
be accessible to non-experts and graduate students.

December 8,
Wednesday
Laura Di Carli,  University of Missouri-Columbia and Florida International University
"Reverse Holder inequalities for linear combinations of spherical harmonics and ultraspherical polynomials"
ABSTRACT: In this talk I will present two main theorems: the first one concerns reverse Holder inequalities for linear combinations of ultraspherical polynomials, and is related to a theorem of N. Kalton and L. Tzafiri. The second one deals with reverse Holder inequalities for spherical harmonics, and improves a Theorem of C. D. Sogge. The proofs of both Theorems rely on precise estimate of a weighted L^p-L^q norm of ultraspherical polynomials. These estimates are quite accurate when the order of the ultraspherical polynomials is much larger than the degree.