Examples of using Analytic functions in English and their translations into Korean
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Analytic functions?
Complex analytic functions.
Livsic took part in the functional analysis seminar and studied analytic functions.
Unlike aggregate functions, analytic functions return all the rows in each group.
He also studied, together with Privalov, boundary uniqueness properties of analytic functions.
Montel worked mostly on the theory of analytic functions of a complex variable.
Analytic functions compute an aggregate value on a group of rows.
The second is to give an account of the theory of Riemann surfaces and analytic functions on Riemann surfaces.
Then he worked on analytic functions, applying results of Mittag-Leffler in a study of the asymptotic investigation of Taylor series.
Poincaré is also considered the originator of the theory of analytic functions of several complex variables.
For mappings in two dimensions, the(orientation-preserving)conformal mappings are precisely the locally invertible complex analytic functions.
In this area he worked on differential equations, analytic functions and functions of several complex variables.
Pincherle contributed to the development and dissemination of Weierstrass 's development of a theory of analytic functions.
I don't know how it happened, but I cannot be satisfied any more with analytic functions and Taylor series… it happened about a year ago….
He published Analytic functions and classes of infinitely differentiable functions as a Rice Institute Pamphlet of 142 pages in 1942.
Contains a collection of interesting and elegant theorems of the theory of analytic functions of a single variable.
Analytic functions of a complex variable were investigated by Euler in a number of different contexts, including the study of orthogonal trajectories and cartography.
In his 1863/64 course on The general theory of analytic functions Weierstrass began to formulate his theory of the real numbers.
This little paperback book contains in 107 pages the core material and usual preliminaries of the standard first course in analytic functions of a complex variable.
One of the works for which Saks is most famous is their joint book Analytic functions which appeared in 1938 as volume eight in the Mathematical Monographs series.
Cartan worked on analytic functions, the theory of sheaves, homological theory, algebraic topology and potential theory, producing significant developments in all these areas.
In particular he attended the one semester course by Weierstrass Introduction to the theory of analytic functions and the notes taken by Hurwitz at this time are reproduced as the book.
He also wrote important works on the theory of analytic functions of a single variable. Darstellung und Begründung einiger meuerer Ergebnisse der Funktiontheorie.
With Hans Grauert, Behnke wrote the paper Analysis in non-compact complex spaces(1960) which was based on a lecture Behnke gave at a conference on analytic functions at Princeton in 1957.
Also important are Plemelj's contributions to the theory of analytic functions which he developed while investigation the problem of uniformization of algebraic functions: .
Montel's idea of normal families proved to be powerful in many connections, for example in the proof ofthe Picard- Landau-Schottky theorems, and it became central in the theory of iterations of analytic functions started by Emile Picard and developed by Fatou and Julia.
Discovered new connections between prime numbers and analytic functions and new rules for the representation of natural numbers through positive integral quadratic forms of an even number of variables.
Its contents were: numbers, the function concept with Weierstrass's power series approach, continuity and differentiability, analytic continuation,points of singularity, analytic functions of several variables, in particular Weierstrass's"preparation theorem", and contour integrals.
The ideas which led him to study the relation between analytic functions and their limit values at the boundaries of their domains came through questions that he was asked by Wladimir Seidel who was a postdoctoral assistant at Harvard at the time.
One of the chief stumbling blocks in such a task is the fact that the notion of derivative is a hereditary property for analytic functions while this is clearly not the case for solutions of general second order elliptic equations.