Complex Analysis

Karl Weierstrass published the first criticism of this assumption in 1870, giving an example of a functional that has a greatest lower bound which is not a minimum value.

Karl Weierstrass is best known for his construction of the theory of complex functions by means of power series.

The study of functions of a complex variable is known as complex analysis

theta functions are special functions of several complex variables

is a highly symmetric holomorphic function on the complex upper half-plane

Further topics studied by Hurwitz include complex function theory

contributed to number theory, graph theory and to the theory of univalent functions

Carl Johannes Thomae was a German mathematician who worked in function theory.

His main works were in the areas of geometry and complex analysis.

Pompeiu's contributions were mainly in the field of mathematical analysis, complex functions theory, and rational mechanics.

Some of his major contributions were in the study of Fourier transforms, complex analysis, non-linear differential equations, number theory, and signal processing.

In addition to his contributions to complex and harmonic analysis

He is known for Morera's theorem in the theory of functions of a complex variable

He is best known for Rouché's theorem in complex analysis

known primarily for his work on complex analysis

worked mainly in function theory

who worked on complex analysis and differential geometry

dissertation entitled Complex Variable and Harmonic Functions Representation by Polynomial Series

and on several complex variables from the point of view of partial differential equations

the leading figure in complex analysis during the 20th century

known for his contribution to mathematical analysis and to the theory of functions of a complex variable

his dissertation about functions with complex arguments

early research into the theory of functions of a complex variable

He also worked on complex function theory, and wrote an important book Teoria delle funzioni di variabili complesse

Pascal was remembered for his work on elliptic functions based on Jacobi theta function.

Almost all Van Vleck's research papers were in the fields of function theory and differential equations.

he wrote the book Théorie des fonctions de variables imaginaires relating to the Imaginary unit

from 1933 he held the chair of the Theory of Functions of a Complex Variable at the Steklov Institute of Mathematics of the USSR Academy of Sciences

made significant contributions to complex analysis

working in complex analysis, geometry, algebra, number theory, Lie groups, and knot theory

He researched mostly on holomorphic functions in complex analysis.

who worked on measure theory, complex analysis, functional analysis and operator theory

He introduced quasi-conformal mappings and differential geometric methods into complex analysis.

geometrical interpretation of complex numbers

In complex analysis, an area of mathematics, Montel's theorem refers to one of two theorems about families of holomorphic function

In complex analysis, a branch of mathematics, the Hadamard three-line theorem is a result about the behaviour of holomorphic funct

rmalism is a technique for applying concepts from complex analysis to the study of the spectrum of operators on Banach spaces and

In mathematics, specifically complex analysis, the Brennan conjecture is a conjecture estimating (under specified conditions) the

ficients of multivalent functions was proposed in complex analysis in 1948 by Adolph Winkler Goodman, an American mathematician.

In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold.

In complex analysis, Runge's theorem (also known as Runge's approximation theorem) is named after the German mathematician Carl Ru

In complex analysis, Mittag-Leffler's theorem concerns the existence of meromorphic functions with prescribed poles.

In complex analysis, a branch of mathematics, Morera's theorem, named after Giacinto Morera, gives a criterion for proving that a

is a result from approximation by polynomials in complex analysis proved by the Armenian mathematician Sergei Mergelyan in 1951.

In complex analysis, a branch of mathematics, Bloch's theorem describes the behaviour of holomorphic functions defined on the unit

complex analysis

complex analysis

complex analysis

complex analysis

complex analysis

functions of several complex variables

His mathematical contributions are connected chiefly with the theory of functions that today is called complex analysis.

He made significant contributions to real and complex analysis, the calculus of variations, and measure theory.

There are two slightly different versions of Abel's test, one is used with series of real numbers, and the other is used with power series in complex analysis.

Calculus and Analysis Complex Analysis

Calculus and Analysis Complex Analysis

Calculus and Analysis Complex Analysis

Weierstrass preparation theorem is a tool for dealing with analytic functions of several complex variables, at a given point

In geometry and complex analysis, a Möbius transformation of the complex plane

transliterated Joukovsky, Joukowski or Zhukovsky) is a conformal map historically used to understand some principles

results in function theory

Édouard Goursat was a French mathematician who is best known for his version of the Cauchy-Goursat theorem stating that the integral of a function round a simple closed contour is zero if the function is analytic inside the contour.

Calculus and Analysis Complex Analysis

Landau gave the first systematic presentation of analytic number theory and wrote important works on the theory of analytic functions of a single variable.

Hermann Hankel was a German mathematician who worked on the theory of complex numbers, the theory of functions and the history of mathematics. He is remembered for the Hankel transform and the Hankel matrix.

Paul Koebe was a German mathematician who worked on complex functions. His colleagues found him brilliant but difficult.

Von Dyck made important contributions to function theory, group theory ( where a fundamental result on group presentations is named after him ) topology and potential theory.