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Analysis Seminars<br />
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Fall 2011
Analysis Seminar
Monday and Wednesday 4th hour (10:40-11:30)
368 Little Hall
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Wednesday 7 December.
- Eric Stetler.
- Positive Definite Completions of Partial Hermitian Matrices.
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Abstract: A partial matrix is a matrix in which some entries are specified and some are not.
Matrix completion problems ask when we can fill in the unspecified entries so that the
matrix we get by doing so has some desired property. We will be using graph theory to determine
which partial Hermitian matrices have positive definite completions.
Monday 5 December.
- Paul Robinson.
- Crinkled arcs.
- Abstract:
A crinkled arc is a continuous ‘simple’ curve in Hilbert space with the property that any two non-overlapping chords are perpendicular. In this expository talk, we show that crinkled arcs exist and that any two (suitably normalized) crinkled arcs are unitarily equivalent. If time permits, we will also discuss some crinkled arc properties.
Wednesday 30 November.
- Adam Adam Broschinski
- Outer Functions II.
Monday 28 November.
- Adam Adam Broschinski
- Outer Functions.
Wednesday 16 November.
- Scott McCullough.
- The Hardy Hilbert spaces of the annulus III – the final installment.
- Abstract: It takes a village of Hardy Hilbert spaces on the annulus to do the work that the classical Hardy space does for the disk. The relationships among these spaces and their reproducing kernels will be described. The Abrahamse Pick interpolation theorem for an annulus is an application.
Monday 14 November.
- Scott McCullough.
- The Hardy Hilbert spaces of the annulus II.
- Abstract: It takes a village of Hardy Hilbert spaces on the annulus to do the work that the classical Hardy space does for the disk. The relationships among these spaces and their reproducing kernels will be described. The Abrahamse Pick interpolation theorem for an annulus is an application.
Wednesday 9 November.
- Scott McCullough.
- The Hardy Hilbert spaces of the annulus.
- Abstract: It takes a village of Hardy Hilbert spaces on the annulus to do the work that the classical Hardy space does for the disk. The relationships among these spaces and their reproducing kernels will be described. The Abrahamse Pick interpolation theorem for an annulus is an application.
Monday 7 November.
- Scott McCullough.
- The Effros-Winkler Hahn-Banach separation theorem and the free TV screen III – the final chapter.
- Abstract: In addition to looking at the theorem, examples of convex free semi-algebraic sets will be examined.
Wednesday 2 November.
- Scott McCullough.
- The Effros-Winkler Hahn-Banach separation theorem and the free TV screen II.
- Abstract: In addition to looking at the theorem, examples of convex free semi-algebraic sets will be examined.
Monday 31 October.
- Scott McCullough.
- The Effros-Winkler Hahn-Banach separation theorem.
- Abstract: In addition to looking at the theorem, examples of convex free semi-algebraic sets will be examined.
Wednseday 19 October.
- Kristin Luery.
- Properties of the Nevanlinna Counting Function III.
Monday 17 October.
- Kristin Luery.
- Properties of the Nevanlinna Counting Function II.
Wednesday 12 October.
- Kristin Luery.
- Properties of the Nevanlinna Counting Function.
Monday 5 October.
- Joel Rosenfeld.
- The absolute continuity of Toeplitz’s matrices III.
- Abstract: A detailed discussion of the paper by
Marvin Rosenblum of the same title will be given.
Monday 26 September.
- Joel Rosenfeld.
- The absolute continuity of Toeplitz’s matrices II.
- Abstract: A detailed discussion of the paper by
Marvin Rosenblum of the same title will be given.
Monday 19 September.
- Joel Rosenfeld.
- The absolute continuity of Toeplitz’s matrices.
- Abstract: A detailed discussion of the paper by
Marvin Rosenblum of the same title will be given.
Wednesday 14 September.
- Mike Jury.
- “Noncommutative” Aleksandrov-Clark measures and function
theory in the unit ball V.
- Abstract: I will describe how some aspects of the de
Branges-Rovnyak theory of backward shift invariant subspaces can be
generalized to higher dimensions. A key tool will be a noncommutative
analog of the Aleksandrov-Clark measures.
Monday 12 September.
- Mike Jury.
- “Noncommutative” Aleksandrov-Clark measures and function
theory in the unit ball IV.
- Abstract: I will describe how some aspects of the de
Branges-Rovnyak theory of backward shift invariant subspaces can be
generalized to higher dimensions. A key tool will be a noncommutative
analog of the Aleksandrov-Clark measures.
Wedenesday 7 September.
- Mike Jury.
- “Noncommutative” Aleksandrov-Clark measures and function theory in the unit ball III.
- Abstract: I will describe how some aspects of the de Branges-Rovnyak theory of backward shift invariant subspaces can be generalized to
higher dimensions. A key tool will be a noncommutative analog of the Aleksandrov-Clark measures.
Wednesday 31 August.
- Mike Jury.
- “Noncommutative” Aleksandrov-Clark measures and function theory in the unit ball II.
- Abstract: I will describe how some aspects of the de Branges-Rovnyak theory of backward shift invariant subspaces can be generalized to
higher dimensions. A key tool will be a noncommutative analog of the Aleksandrov-Clark measures.
Monday 29 August.
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