Complex Analysis and Operator Theory
Thursday 4pm-5pm (Place: UH 4170)
April 23, 2020
Complex symmetry of weighted composition operators
Uthpala Nawalage (University of Toledo)
Abstract. Dissertation public talk.
April 9, 2020
Toeplitz operators via differential equations
Akaki Tikaradze (University of Toledo)
Abstract. I will discuss a link between Toeplitz operators with polyanalytic symbols and linear holomorphic differential equations. This will allow proving some operator theoretic results based on elementary facts about differential equations.
April 2, 2020
Universality of automorphisms on the ball of bounded holomorphic functions on the polydisk
Tim Clos (Kent State University)
Abstract. Given a sequence of automorphisms of the polydisk, we show that the associated composition semigroup homomorphisms on the ball of bounded holomorphic functions on the polydisk admit a universal inner function if a certain condition on the automorphisms is satisfied.
March 5, 2020
Bekollé-Bonami estimates on some pseudoconvex domains
Zhenghui Huo (University of Toledo)
Abstract. In the 80s, Bekollé and Bonami gave a necessary and sufficient condition for the boundedness of the Bergman projection on the weighted $L^p$ space of the unit ball. Recently, using dyadic harmonic analysis technique, weighted $L^p$ estimates were obtained for the Bergman projection on for example, the upper half plane, the unit ball, and the Hartogs triangle. In this talk, I will present sharp estimates for the weighted $L^p$ norm of the projection on a class of pseudoconvex domains. I will also explain the dyadic operator technique used in the proof. This talk is based on joint work with Nathan Wagner and Brett Wick.
February 27, 2020
Laurent series in spaces of holomorphic functions
Anirban Dawn (Central Michigan University)
Abstract. Let $X$ be a linear space of holomorphic functions on a Reinhardt domain in $\mathbb{C}^n$. We study the convergence and summability (in the topology of $X$) of Laurent series of functions in $X$. We introduce the principle of missing monomials and discuss some of its applications. We also discuss the notions of absolute and unconditional convergence of Laurent series in locally convex spaces and show that holomorphic functions smooth up to the boundary have Laurent series which converge unconditionally.
February 20, 2020
The numerical range of the product of a composition operator with the adjoint of a composition operator
John Clifford (University of Michigan at Dearborn)
Abstract. In this talk we will look at the numerical range of the operator $C^*_{b \varphi^m}C_{a \varphi^n}$ and $C_{a \varphi^n}C^*_{b \varphi^m}$, where $\varphi$ is an inner function fixing the origin, and $a$ and $b$ are points in the open unit disc, on the Hardy space. The numerical range of an operator $T$ acting on a complex Hilbert space $H$ is the set in the complex plane
$$W(T) = \{ \langle Tx,x\rangle: \|x\|=1\,\, \text{and} \,\, x \in H\}.$$
In the case $|a|=|b|=1$ we compute the numerical range. Also if the magnitude of $a^mb^n$ is sufficiently small we are able to compute the numerical range.
This is joint work with Michael Dabkowski and Alan Wiggins.
This is joint work with Michael Dabkowski and Alan Wiggins.
February 6, 2020
Norms of evaluation functionals on Bergman spaces
Trieu Le (University of Toledo)
Abstract. It is well known that for any integer $m$ and any complex number $\alpha$, the map $f\mapsto f^{(m)}(\alpha)$ is a bounded linear functional on the Bergman space $A^{p}$ ($0 < p < \infty$) over the unit disk. We shall discuss the problem of finding the norm of such a functional.
Forthcoming
November 14, 2019
An application of Hörmander's $L^2$ methods
Yifei Pan (Purdue University Fort Wayne)
Abstract. Using Hörmander's $L^2$ methods from several complex variables we prove existence of right inverse of well known operators in a weighted Hilbert space which in particular includes the Laplace operator.
November 7, 2019
Weak-type estimates for the Bergman projection on the polydisc and the Hartogs triangle, part II
Zhenghui Huo (University of Toledo)
Abstract. In this talk, I will discuss about the weak-type regularity of the Bergman projection on the polydisc and the Hartogs triangle. We will see from these two cases that both the product structure and the boundary singularity may affect the weak-type behavior of the projection.
October 31, 2019
Weak-type estimates for the Bergman projection on the polydisc and the Hartogs triangle
Zhenghui Huo (University of Toledo)
Abstract. In this talk, I will discuss about the weak-type regularity of the Bergman projection on the polydisc and the Hartogs triangle. We will see from these two cases that both the product structure and the boundary singularity may affect the weak-type behavior of the projection.
October 24, 2019
Segal--Bargmann transforms and Hilbert spaces of entire functions
Luan M. Doan (University of Notre Dame)
Abstract. The Segal--Bargmann transforms have been playing important roles in complex analysis and mathematical physics, especially an area called geometric quantization. In the operator-theoretic settings, they can be described as unitary operators from Hilbert spaces of square summable functions $L^2(M,dx)$ to a Hilbert space of entire functions $\mathcal{H}L^2(X,d\mu)$, where $M$ is a so-called configuration space, $X$ is a ``complexified" version of $M$, and $\mu$ is an appropriate measure. A typical example is when $M=\mathbb{R}^n$, $X=\mathbb{C}^n$, and $\mu$ is the (complex) heat-kernel. We study in details these transforms for the case $M=\mathbb{R}^n$, possibly generalize to Lie groups and introduce some interesting open questions.
October 17, 2019
On regularity of the Berezin transform, Part II
Sonmez Sahutoglu (University of Toledo)
Abstract. For the open unit disk $\mathbb{D}$ in the complex plane, it is well known that if $\varphi \in C(\overline{\mathbb{D}})$ then its Berezin transform $\widetilde{\varphi}$ also belongs to $C(\overline{\mathbb{D}})$. We say that
$\mathbb{D}$ is BC-regular. We study BC-regularity of more general domains in $\mathbb{C}^n$ and show that the boundary geometry
plays an important role. This is joint work with Zeljko Cuckovic.
September 26, 2019
On regularity of the Berezin transform
Sonmez Sahutoglu (University of Toledo)
Abstract. For the open unit disk $\mathbb{D}$ in the complex plane, it is well known that if $\varphi \in C(\overline{\mathbb{D}})$ then its Berezin transform $\widetilde{\varphi}$ also belongs to $C(\overline{\mathbb{D}})$. We say that
$\mathbb{D}$ is BC-regular. We study BC-regularity of more general domains in $\mathbb{C}^n$ and show that the boundary geometry
plays an important role. This is joint work with Zeljko Cuckovic.
September 5, 2019
ORGANIZATIONAL MEETING
This webpage uses the bootstrap framework.