Complex Analysis Seminar

Next Seminar :

Tuesday October 18
1:30-2:30 C-401 Padelford

Stephan Garcia
U.C.S.B.

Holomorphic functions with real boundary values

     We discuss a constructive infinite product expansion for holomorphic functions of bounded characteristic (a standard growth condition) on the unit disk whose nontangential limiting values on the unit circle are real almost everywhere.  We sketch a few elements of the construction, which relies on the Cauchy A-integral. Although such functions might appear little more than a classical curiosity, they have many applications, including a complete description of "pseudocontinuable functions," an analog of Beurling's theorem for the backward shift operator on the Hardy spaces, the parametrization of the kernels of Toeplitz operators, and an analog of the Riesz-Szego projection for 0 < p < 1.

Everyone is welcome to attend. If you are a student and are interested in receiving credit for attendance, please see
Don Marshall or Steffen Rohde.

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