| Complex
Analysis Seminar |
| Abstract: We establish some basic properties of BMO${}^p$ for $p \geq 1$ and complete the characterization of bounded and compact Toeplitz operators with BMO${}^1$ symbols on the Segal-Bargmann space of Gaussian square-integrable entire functions on $\mathbb{C}^n$. This is a joint work with L. A. Coburn and J. Isralowitz. |
| Abstract: If T is a contraction, then (Case 1) T is a completely non-unitary contraction with a non-trivial algebraic element, or (Case 2) T is a completely non-unitary contraction without a non-trivial algebraic element, that is, every non-zero element in H is transcendental with respect to T, or (Case 3) T is not completely non-unitary. We discuss the invariant subspace problem for operators of (Case 1) or (Case 3). |
| Abstract:
I will present part of the paper by Arazy and Englis with the
same title, published in the Ann. Inst. Fourier (Grenoble), 2001. |
| Abstract:
T. Carleman (1927) showed that for
any continuous function f on the real line and any strictly positive
and continuous error function $e$, there exists an entire function $h$
such that $|h(x)-f(x)|\leq e(x)$ for all real $x.$ We show how this
result can be extended to approximation on totally real sets in Stein
manifolds. |
| Abstract: The
following question will be
discussed: Is the Bergman projection ``regular" on smooth bounded pseudoconvex domains in $\mathbb{C}^n$? This question has been answered by several authors in $\mathbb{C}^2.$ A partial answer will be given on domains in $\mathbb{C}^n$ for $n\geq 3.$ |
| Abstract:
In
this talk, an
affirmative answer is given to one of the questions, posed by
P. R. Halmos. |
| Abstract:
In
this talk, an
affirmative answer is given to one of the questions, posed by
P. R. Halmos. |
| Abstract: Let f be a function that is continuous on the closed polydisc $\overline{D}^n$. I will discuss the compactness of the Toeplitz operator $T_f$ and of the Hankel operator $H_f$ on the Bergman space $A^2(D^n).$ |
| Abstract:
We
give examples of weights, on the unit disc, for which the weighted
Bergman projection is only bounded on $L^p$ for a finite range values
of
p. This range is more than just $p=2$ but smaller than the interval
$(1,\infty).$ |
| Abstract: In this talk we give a new formula for the essential norms of the composition operators between Bloch type spaces in terms of the norms of the n-th power of the inducing map. New characterizations for bounded and compact composition operators between Bloch type spaces invovling the same terms are also given. |
| Abstract:
In
this talk plurisubharmonic hull,
existence of analytic discs, and the $\bar\partial$-problem will
be defined.
Furthermore, some relations between them will be mentioned. |
| Abstract: I will introduce few types of extension problems for holomorphic functions on complex manifolds and explain relationships between them. |