The doctoral dissertation in the field of Mathematics will be examined at the Faculty of Science, Forestry and Technology, Joensuu campus.
What is the topic of your doctoral research? Why is it important to study the topic?
My doctoral research focuses on Bergman reproducing kernels, the understanding of which is fundamental in operator theory and complex analysis, as they provide a concrete manifestation of the analytic structure of Bergman spaces and the properties of their related operators. Classical operators including Bergman projections, Toeplitz operators, Hankel operators, and Berezin transforms, can be explicitly expressed in terms of the reproducing kernel. Their mapping behaviors, such as boundedness, compactness, and Schatten-class membership, rely on precise kernel estimates. Consequently, analyzing reproducing kernels provides a unified approach for tackling interrelated problems in function theory, operator theory, and harmonic analysis within the context of Bergman spaces.
What are the key findings or observations of your doctoral research?
In the doctoral research, we establish sharp and novel estimates for Bergman reproducing kernels, and equivalent norms for several classical analytic function spaces in terms of fractional derivatives. These results are systematically applied to the study of the (analytic) tent spaces and the classical operators acting on them.
What are the key research methods and materials used in your doctoral research?
During my doctoral research, a sharp off-diagonal pointwise upper estimate for the Bergman reproducing kernel induced by a radial doubling weight in the unit disc is essential for addressing a wide range of iterated problems in operator theory and complex analysis. We illustrated its utility via multiple applications. An easy application yields an optimal integral estimate for certain modified Bergman kernels, which further motivated the study of the two-weight fractional derivatives. These technical tools have become indispensable in our study of analytic tent spaces.
The doctoral dissertation of Siyu Wang, DSc, entitled Bergman kernel estimates and fractional derivatives with applications to operator theory will be examined at the Faculty of Science, Forestry and Technology, Joensuu campus. The opponent will be Professor Alexandru Aleman, Lund University, Sweden, and the custos will be Professor Jouni Rättyä, University of Eastern Finland. Language of the public defence is English.
For further information, please contact:
Siyu Wang, [email protected]
