Abstract. In a variety of classical function spaces, some properties of a given operator can be analyzed by examining only its behavior on the normalized reproducing kernel. In this talk, we consider conditions for the boundedness and compactness of operators on the Bergman space of the Thullen domain. We give a sufficient condition for the boundedness. Under this sufficient condition, we show that the behavior of operator on the normalized Bergman kernels determines the compactness of the operator. We will discuss several results about Toeplitz operators and Hankel operators along this line. This work is joint with Brett Wick.

Abstract. An important open problem in multivariable operator theory and function theory of several complex variables is the problem of classification or an explicit description (in some sense) of all invariant subspaces of the Hardy space $H^2(D^n)$ on the polydisc $D^n$ given by W. Rudin [1, p.78]. This problem has been extensively studied by various authors in different context, but it is still open. Hence we need good examples to help us understand the structure of invariant subspaces of $H^2(D^n)$. In this talk, we completely classify the singly-generated invariant subspace and define two types of invariant subspaces of $H^2(D^n)$. Then, we give a characterization of these types invariant subspaces in view of the Beurling-Lax-Halmos Theorem.

References
[1] W. Rudin, Function Theory in Polydisks, W.A.Benjamin, Inc., New York-Amsterdam, 1969.

Abstract. This is an introductory talk about the restriction operator on Bergman spaces and its relation to Hankel operators. This is joint work with Debraj Chakrabarti.

Abstract. We consider Laurent series of holomorphic functions on Reinhardt domains and obtain a condition for the density of Laurent polynomials in Banach spaces of holomorphic functions on Reinhardt domains. Using the method of proof for this condition, we obtain a generalization of a result of Sibony on the behavior of holomorphic functions smooth up to the boundary on the Hartogs triangle.

Abstract. This is an introductory talk about the restriction operator on Bergman spaces and its relation to Hankel operators. This is joint work with Debraj Chakrabarti.

Abstract. We will prove in terms of so-called Berezin symbols some theorems for Borel summability method for sequences and series of complex numbers, and give a new Tauberian type theorem for Borel summability.

Abstract. We will define complex symmetry of bounded operators on a complex Hilbert space and discuss conditions for a composition/weighted composition operator to be complex symmetric with respect to a specific conjugation on Hardy and Bergman spaces.

Abstract. We will define complex symmetry of bounded operators on a complex Hilbert space and discuss conditions for a composition/weighted composition operator to be complex symmetric with respect to a specific conjugation on Hardy and Bergman spaces.

Abstract. An inner function is a bounded holomorphic function on the unit disk whose values have modulus one almost everywhere on the unit circle. Inner functions play an important role in function theory and operator theory. Recent work of Beneteau et al. studies inner functions in the more general setting of weighted Hardy spaces. Motivated by their results, we shall discuss a construction of such inner functions.