| Analysis Research Group | |
| Analysis
Seminar, Fall 2009 Wednesday 4:30 - 5:20 pm Cardwell 120 (except when otherwise noted) |
Organizer: Charles Moore Previous semesters: Spring 06 Fall 06 Spring 07 Fall 07 Spring 08 Fall 08 Spring 09 |
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Monday, September 14- Irina MItrea,
Worcester Polytechnic Institute On the mixed problem for second order elliptic systems In this talk I will discuss well-posedness results for boundary value problems for second order elliptic operators with mixed Dirichlet and Neumann type boundary conditions in irregular domains. Wednesday, September 23- Mukta Bhandari Good-lambda inequalities and potentials for non-doubling measures We establish a good-lambda inequality relating the distribution functions of a Riesz potential and a fractional maximal function. This is extended to weights. We also derive potential inequalities as an application. Tuesday, September 29- Loredana Lanzani, University of Arkansas Div-Curl type inequalities for Hodge systems: Old and New I will review a 2005 result (joint with E.M. Stein)
concerning
L^1-to-L^p inequalities for the canonical solution of the classical
Hodge system: dZ=f; d^*Z=g with the data subject to the compatibility
conditions: df=0; d^*g=0. (Here d denotes the exterior derivative
operator in Euclidean space). I will then discuss work in
progress with A. Raich that aims at generalizing these inequalities to
Hodge-type systems for higher order differential operators.
Time and Location: 10:30 AM, Military Science 210 Wednesday, October 7- no seminar - meeting of analysis faculty Wednesday, October 14- Santosh Ghimire Tail LILs for sums of Rademacher functions We show a tail law of the iterated logarithm for sums of Rademacher functions Wednesday, October 28- Diego Maldonado Weighted multilinear Poincaré inequalities, Part I. Wednesday, November 4- Virginia Naibo Weighted multilinear Poincaré inequalities, Part II. Friday, November 13- John J. Benedetto, University of Maryland Frames for wavelet sets and classification of spectral data The theme is the role of frames in providing effective tools to deal with large data sets. There are two case studies. The mathematical tools are wavelet theory, Fourier analysis, and frame potential energy analysis. The first case constructs simple, smooth dyadic wavelet frames for Euclidean space from ONE wavelet. A surprising phenomenon, called a frame bound gap arises; and these gaps are analyzed and computed. The second case designs a classification algorithm, where frames are required to balance classification with dimension reduction. The technology naturally combines frame potential energy with discrete Wiener amalgam spaces. Examples include the analysis of hyperspectral and retinal data. Wednesday, November 18- A.G. Ramm Implicit function theorem via the Dynamical Systems Method (DSM) The Dynamical Systems Method (DSM) for solving a class of nonlinear operator equations F (u) = f in a Hilbert space H is discussed. Sufficient conditions are given for an implicit function theorem to hold. The result is established by an application of the version of the Dynamical Systems Method (DSM), a Newton-type method. This result allows one to solve the above equations in the case when the Fréchet derivative F'(u) of the nonlinear operator F is a smoothing operator, so that its inverse is an unbounded operator. The DSM version we discuss is: u(t) = -[F '(u(t)]^-1 (F(u(t)) - f ), u(0) = u_0 . Under suitable assumptions we prove that a) the above problem has a global solution, b) there exists u(\infty), and c) F (u(\infty)) = f . Wednesday, December 2- Petronela Radu, University of Nebraska, Lincoln Wednesday, December 9 - Erika Ward, University of Kansas |