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Title: On Contractive extensions in Banach spaces Speaker: Boris Shekhtman Time: 4:00pm–5:00pm Place: CMC 130
Let \(V\subset W\subset X\) be Banach spaces.
I plan to talk about a relationship between projectional constants $$\lambda(V,X) := \inf\left\{\|P\|:P\text{ is a projection from $X$ onto }V\right\}$$ and extension constants $$\lambda(V,W,X) := \inf\left\{\|E\|:E\to W,\ E_{\left|V\right.}=I\right\}$$ and answer some interesting (to me) questions about this relationship.
Title: On the zero sets of bounded analytic functions, Part II Speaker: Arthur Danielyan Time: 4:00pm–5:00pm Place: CMC 130
Title: On the zero sets of bounded analytic functions Speaker: Arthur Danielyan Time: 4:00pm–5:00pm Place: CMC 130
In this talk it will be shown that the F. and M. Riesz boundary uniqueness theorem directly follows from Fatou's theorem on the almost everywhere existence of the radial limits. Some boundary properties of Blaschke products will be considered too.
Title: Weird extremal problems in Hardy spaces, minimal projections, Beurling’s theorem in the \(H^p\) setting and zeros of optimal polynomial approximants, Part II Speaker: Dima Khavinson Time: 4:00pm–5:00pm Place: CMC 130
Title: Weird extremal problems in Hardy spaces, minimal projections, Beurling’s theorem in the \(H^p\) setting and zeros of optimal polynomial approximants Speaker: Dima Khavinson Time: 4:00pm–5:00pm Place: CMC 130
The Beurling invariant subspace theorem is well known to hold in the \(H^p, p>0\) setting, however the proof for \(p\ne2\) is different. Attempting to mimic the Hilbert space proof leads to interesting questions concerning minimal projections in the \(L^p\) metric, intricate extremal problems and inequalities and the problem of zeros of optimal polynomial approximants in \(H^p, p\ne 2\), setting. Parts of this work stems from a joint project with C. Bénéteau, R. Cheng, C. Felder, M. Manolaki and K. Maronikolakis.
Title: On the boundary behavior of analytic functions Speaker: Arthur Danielyan Time: 4:00pm–5:00pm Place: CMC 130
We present a new property of bounded analytic functions in the unit disc which directly implies some classical theorems due to N. N. Lusin, A. J. Lohwater and G. Piranian, and A. Beurling. An application of the method for the concept of natural boundary of power series will be given. (The students familiar with the rudiments of analytic function theory and Lebesgue measure will be able to follow the talk and are welcome.)