Boyadzhiev, Khristo N. Integral representation of functions on sectors, functional calculus and norm estimates. (English) Zbl 1046.47027 Collect. Math. 53, No. 3, 287-302 (2002). Summary: We find an explicit integral representation for bounded holomorphic functions \(f(z)\) on sectors \(|\text{Arg} (z)|<\psi\) in terms of the kernel \(z(z+\lambda)^{-2}\) and present some applications to operator theory. Namely, given a sectorial operator \(A\), we define the functional calculus \(A\to f (A)\) and find pointwise estimates and moment type inequalities for \(\| f(A)x\|\). We show that sectorial operators have a bounded \(H^\infty\)-functional calculus on a dense subspace. We also find exact estimates for the norm \(\| e^{-\lambda A}\|\) of analytic semigroups. Cited in 2 Documents MSC: 47B44 Linear accretive operators, dissipative operators, etc. 30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane 47A60 Functional calculus for linear operators 47D06 One-parameter semigroups and linear evolution equations Keywords:sectorial operator; momentum inequality PDFBibTeX XMLCite \textit{K. N. Boyadzhiev}, Collect. Math. 53, No. 3, 287--302 (2002; Zbl 1046.47027) Full Text: EuDML