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Several Complex Variables Seminar

Date: September 20, 2017

Time: 2:00PM - 2:50PM

Location: BLOC 628

Speaker: Yi Wang, TAMU


Title: On the p-essential normality of principal submodules of the Bergman module on strongly pseudoconvex domains

Abstract: We show that under a mild condition, a principal submodule of the Bergman module on a strongly pseudoconvex domain, generated by a holomorphic function defined on a neighborhood of its closure, is p essentially normal for p>n. Two main ideas are involved in the proof. The first is that a holomorphic function defined in a neighborhood 'grows like a polynomial'. This is illustrated in a key inequality that we prove in our paper. The second is that commutators of Toeplitz operators behave much better than the operator themselves. This seminar is joint with the Non-Commutative Geometry Seminar.