Dictionary

analytic function en · NOUN

Meanings

1. Any smooth (infinitely differentiable) function f, defined on an open set D⊆ℂ( textit or⊆ℝ), whose value in some neighbourhood of any given point x_0∈D is given by the Taylor series ∑ₙ₌₀ ᪲(f⁽ⁿ⁾(x_0))/(n!)(x-x_0)ⁿ.
   • There is a large and important literature concerned with the question of how to characterize precisely the boundary values of analytic functions. For example, when the analytic functions are of Hardy Class H#42; in a half plane, then their boundary values are attained in the L2 norm and, in fact, the analytic function can be reproduced by a Cauchy integral of the boundary value. 1966, E. J. Beltrami, M. R. Wohlers, Distributions and the Boundary Values of Analytic Functions, Academic Press, page vii:
   • 2000, Vladimir V. Mityushev, Sergei V. Rogosin, Constructive Methods for Linear and Nonlinear Boundary Value Problems for Analytic Functions: Theory and Applications, Chapman & Hall / CRC, page v, Thus we have limited ourselves by boundary value problems for analytic functions, and some related problems. The constructive ideas are always in our mind, so, the basic goal of this book is to be useful for experts in analytic function theory and for nonspecialists in it, and even for non-mathematicians who apply these methods in their research.
   • 2010, Emmanuel Fricain, Andreas Hartmann, Regularity on the Boundary in Spaces of Holomorphic Functions on the Unit Disk, Javad Mashreghi, Thomas Ransford, Kristian Seip (editors, Hilbert Spaces of Analytic Functions, American Mathematical Society, page 91, We review some results on regularity on the boundary in spaces of analytic functions on the unit disk connected with backward shift invariant subspaces in Hᵖ.
2. window function

Forms

Deriveds

complex analytic function · real analytic function

Hypernyms

function (analysis)

Hyponyms

real analytic function (analysis) · complex analytic function (analysis) · monogenic analytic function (analysis)

Translations (10)

cmn 解析函數 /解析函数 (mathematical function) · hu analitikus függvény (mathematical function) · pl funkcja analityczna (mathematical function) · cs analytická funkce (mathematical function) · sh analitička funkcija (mathematical function) · pt função analítica (mathematical function) · fi analyyttinen funktio (mathematical function) · sv analytisk funktion (mathematical function) · is raunfágað fall (mathematical function) · tl suriing kabisa (mathematical function)