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SUMMARY:Hyponormal quantization of planar domains - Mihai Putinar (Univers
 ity of California\, Santa Barbara\; Newcastle University)
DTSTART:20190912T130000Z
DTEND:20190912T140000Z
UID:TALK129460@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:By replacing the identity operator in Heisenberg commutation r
 elation<br> [T*\,T]=I by a rank-one projection one unveils an accessible s
 pectral analysis classification<br> with singular integrals of Cauchy type
  as generic examples. An inverse spectral problem for this class<br> of (h
 yponormal) operators can be invoked for encoding and decoding (partial) da
 ta of 2D pictures carrying a grey shade function.<br> An exponential trans
 form\, the two dimensional analog of a similar operation on Cauchy integra
 ls<br> introduced by A\, Markov in his pioneering work on 1D moment proble
 ms\, provides an effective dictionary<br> between "pictures" in the freque
 ncy domain and "matrices" in the state space interpretation.<br> A natural
  Riemann-Hilbert problem lies at the origin of this kernel with potential 
 theoretic flavor. Quadrature domains for<br> analytic functions are single
 d out by a rationality property of the exponential transform\, and hence a
 n exact reconstruction<br> algorithm for this class of black and white sha
 pes emerges. A two variable diagonal Pade approximation scheme and <br> so
 me related complex orthogonal polynomials enter into the picture\, with th
 eir elusive zero asymptotics.<br> Most of the results streaming from two d
 ecades of joint work with Bjorn Gustafsson.<br>
LOCATION:Seminar Room 1\, Newton Institute
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