Results 241 to 250 of about 138,862 (288)
Some of the next articles are maybe not open access.
2014
Holomorphic functions on a polydisc are represented by the Cauchy integral of their values on the distinguished boundary of the polydisc.
openaire +1 more source
Holomorphic functions on a polydisc are represented by the Cauchy integral of their values on the distinguished boundary of the polydisc.
openaire +1 more source
Cauchy integrals forL 2 functions
Archiv der Mathematik, 1988Let \(c(z,\zeta)=(\zeta -z)^{-1}\) for z,\(\zeta\in {\mathbb{C}}\). Let D be a bounded regular plane region with analytic boundary \(\partial D\), and let CF denote the Cauchy transform \[ (CF)(z)=(2\pi i)^{- 1}\oint_{\partial D}c(z,\zeta)F(\zeta)d\zeta \quad (z\in D) \] of \(F\in L^ 2(\partial D)\). Evidently, C maps \(L^ 2(\partial D)\) into \(H^ 2(D)
openaire +2 more sources
Cauchy’s Integral Theorem. Proof of Theorem 3.1. Cauchy’s Integral Formula
2017We will now give further applications of Theorem 9.1. In what follows we often consider functions holomorphic on domains containing the closure \( \overline{D} \) of a domain D. For such a function f we write \( f \in H(\overline{D})\).
openaire +1 more source
Cauchy Type Integral Equations
2000In this chapter we study various singular integral equations with kernels of the Cauchy type, starting from the most basic Cauchy type integral equation.
Ricardo Estrada, Ram P. Kanwal
openaire +1 more source
The American Mathematical Monthly, 2007
Theorem. Let D be a domain in the complex plane, f(z) an analytic function in D, C a closed curve that is described by a continuously differentiable function z(s) (0 < s < 1) with z(0) = z(l) and zf(0) = z'(\). Suppose that C is homotopic in D to a point, meaning that there is a continuous function z(s, t) (0 < s < I, 0 < t < 1) with z(0, t) = z(l, t ...
openaire +1 more source
Theorem. Let D be a domain in the complex plane, f(z) an analytic function in D, C a closed curve that is described by a continuously differentiable function z(s) (0 < s < 1) with z(0) = z(l) and zf(0) = z'(\). Suppose that C is homotopic in D to a point, meaning that there is a continuous function z(s, t) (0 < s < I, 0 < t < 1) with z(0, t) = z(l, t ...
openaire +1 more source
An overview of real‐world data sources for oncology and considerations for research
Ca-A Cancer Journal for Clinicians, 2022Lynne Penberthy +2 more
exaly
Cauchy: Differentiation and Integration
2015Here we look at Cauchy’s treatment of differentiation and integration. Cauchy not only reversed a century of tradition that regarded integration as essentially the inverse of differentiation, he brought a raft of new ideas and theorems to the subject.
openaire +1 more source
The mechanisms of integral membrane protein biogenesis
Nature Reviews Molecular Cell Biology, 2021Ramanujan Shankar Hegde, Robert J Keenan
exaly
Planning for tomorrow: global cancer incidence and the role of prevention 2020–2070
Nature Reviews Clinical Oncology, 2021Isabelle Soerjomataram, Frank Bray
exaly
Antibiofilm activity of host defence peptides: complexity provides opportunities
Nature Reviews Microbiology, 2021, Morgan A Alford, Evan F Haney
exaly