Properties of singular integral operators S_α,β

2015/05/20 by Amit Samanta, Amit K. Samanta, Samanta, Amit +2
Mathematics · #Algebraic and Geometric Analysis #Approximation Theory and Sequence Spaces #Holomorphic and Operator Theory #math.FA #msc:30D55 #msc:45E10 #msc:47B20 #msc:47B35

paper · pdf · doi:10.48550/arxiv.1505.05326

19 pages

arxiv created 2015/05/20 · arxiv updated 2015/05/21

Abstract

For α, β∈ L^∞ (S¹), the singular integral operator S_α,β on L² (S¹) is defined by S_α,βf:= αPf+βQf, where P denotes the orthogonal projection of L²(S¹) onto the Hardy space H²(S¹), and Q denotes the orthogonal projection onto H²(S¹)^⊥. In a recent paper Nakazi and Yamamoto have studied the normality and self-adjointness of S_α,β. This work has shown that S_α,β may have analogous properties to that of the Toeplitz operator. In this paper we study several other properties of S_α,β.

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