走向现代数学学术报告 - Prof. Aristomenis G. Siskakis（No. 967)

报告题目：Holomorphic semigroups and induced operator theory

报 告 人：Prof. Aristomenis G. Siskakis (University of Thessaloniki, Greece)

邀 请 人：娄增建 教授

报告时间：2026年10月13日 16：00

腾讯会议ID：734-997-997

报告摘要：A holomorphic semigroup on the unit disc 𝔻 is a family of holomorphic self maps of 𝔻 with the properties:

(i), the identity map on 𝔻,

(ii) for ,

(iii) The map is jointly continuous on .

Such a family induces a semigroup of composition operators, and also of weighted composition operators

,    ,

where a cocycle for , on spaces of holomorphic functions on 𝔻, such as Hardy, Bergman, Dirichlet and on other spaces.

In principle, operator theoretic properties of the operator semigroups , on are mirrored to analytic properties of , , such as the infinitesimal generator ，the inducing Koenings map etc, thus connecting Operator Theory to Geometric Function Theory on 𝔻.

In this talk we will describe the development and by-products of the theory of composition semigroups, the connection to some classical operators such as the Cesàro operator and Volterra operators, and will also describe related recent results.

报告人简介：

I. Education

Undergraduate  B.S. in Mathematics, University of Athens, Greece

1979–1985: Graduate Studies University of Illinois at Urbana-Champaign, USA

1985: Ph.D. in Mathematics, University of Illinois at Urbana-Champaign, USA

II. Professional Experience

1985–1989: Postdoctoral Positions , Indiana University, Purdue University Indianapolis, Texas A&M University, Rutgers University

1989–1990: Assistant Professor, New Mexico State University, USA

1990–1994: Assistant Professor, Aristotle University of Thessaloniki

1995–2001: Associate Professor, Aristotle University of Thessaloniki

1997–1998: Visiting Professor, University of North Carolina at Chapel Hill, Purdue University

2001–Present: Professor Aristotle University of Thessaloniki

III. Research Interests: Complex Analysis, Operator Theory

IV. Selected Publications

1987, Composition semigroups and the Cesàro operator on Hᵖ, Journal of London Mathematical Society (2) 36, 153–164

1995, An integral operator on Hᵖ, Complex Variables Theory and Applications 28, 149–158 (with A. Aleman)

1997, Integration operators on Bergman spaces, Indiana University Mathematics Journal 46, 337–356 (with A. Aleman)

2001, Hausdorff matrices and composition operators, Illinois Journal of Mathematics 45, 757–773 (with P. Galanopoulos)

2016, The multiplicative Hilbert matrix, Advances in Mathematics 302, 410–432 (with F. Brevig, K.M. Perfekt, K. Seip, D. Vukotic)

2020, Composition operators and the Hilbert matrix, Studia Math. 140 (2000), no. 2, 191–198 (with Diamantopoulos, E.)