• Title, Summary, Keyword: analytic function

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ANALYTIC AND GEOMETRIC PROPERTIES OF OPEN DOOR FUNCTIONS

  • Li, Ming;Sugawa, Toshiyuki
    • Journal of the Korean Mathematical Society
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    • v.54 no.1
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    • pp.267-280
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    • 2017
  • In this paper, we study analytic and geometric properties of the solution q(z) to the differential equation q(z) + zq'(z)/q(z) = h(z) with the initial condition q(0) = 1 for a given analytic function h(z) on the unit disk |z| < 1 in the complex plane with h(0) = 1. In particular, we investigate the possible largest constant c > 0 such that the condition |Im [zf"(z)/f'(z)]| < c on |z| < 1 implies starlikeness of an analytic function f(z) on |z| < 1 with f(0) = f'(0) - 1 = 0.

Convolution product and generalized analytic Fourier-Feynman transforms

  • Chang, Seung-Jun
    • Communications of the Korean Mathematical Society
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    • v.11 no.3
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    • pp.707-723
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    • 1996
  • We first define the concept of the generalized analytic Fourier-Feynman transforms of a class of functionals on function space induced by a generalized Brownian motion process and study of functionals which plays on important role in physical problem of the form $ F(x) = {\int^{T}_{0} f(t, x(t))dt} $ where f is a complex-valued function on $[0, T] \times R$. We next show that the generalized analytic Fourier-Feynman transform of the convolution product is a product of generalized analytic Fourier-Feynman transform of functionals on functin space.

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ANALYTIC OPERATOR-VALUED GENERALIZED FEYNMAN INTEGRALS ON FUNCTION SPACE

  • Chang, Seung Jun;Lee, Il Yong
    • Journal of the Chungcheong Mathematical Society
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    • v.23 no.1
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    • pp.37-48
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    • 2010
  • In this paper we use a generalized Brownian motion process to defined an analytic operator-valued generalized Feynman integral. We then obtain explicit formulas for the analytic operatorvalued generalized Feynman integrals for functionals of the form $$F(x)=f\({\int}^T_0{\alpha}_1(t)dx(t),{\cdots},{\int}_0^T{\alpha}_n(t)dx(t)\)$$, where x is a continuous function on [0, T] and {${\alpha}_1,{\cdots},{\alpha}_n$} is an orthonormal set of functions from ($L^2_{a,b}[0,T]$, ${\parallel}{\cdot}{\parallel}_{a,b}$).

ANALYTIC TRAVELLING WAVE SOLUTIONS OF NONLINEAR COUPLED EQUATIONS OF FRACTIONAL ORDER

  • AN, JEONG HYANG;LEE, YOUHO
    • Honam Mathematical Journal
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    • v.37 no.4
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    • pp.411-421
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    • 2015
  • This paper investigates the issue of analytic travelling wave solutions for some important coupled models of fractional order. Analytic travelling wave solutions of the considered model are found by means of the Q-function method. The results give us that the Q-function method is very simple, reliable and effective for searching analytic exact solutions of complex nonlinear partial differential equations.

OPERATOR-VALUED FUNCTION SPACE INTEGRALS VIA CONDITIONAL INTEGRALS ON AN ANALOGUE WIENER SPACE II

  • Cho, Dong Hyun
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.3
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    • pp.903-924
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    • 2016
  • In the present paper, using a simple formula for the conditional expectations given a generalized conditioning function over an analogue of vector-valued Wiener space, we prove that the analytic operator-valued Feynman integrals of certain classes of functions over the space can be expressed by the conditional analytic Feynman integrals of the functions. We then provide the conditional analytic Feynman integrals of several functions which are the kernels of the analytic operator-valued Feynman integrals.

ANALYTIC OPERATOR-VALUED FUNCTION SPACE INTEGRAL REPRESENTED AS THE BOCHNER INTEGRAL:AN$L(L_2)$ THEORY

  • Chang, Kun-Soo;Park, Ki-Seong;Ryu, Kun-Sik
    • Communications of the Korean Mathematical Society
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    • v.9 no.3
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    • pp.599-606
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    • 1994
  • In [1], Cameron and Storvick introduced the analytic operator-valued function space integral. Johnson and Lapidus proved that this integral can be expressed in terms of an integral of operator-valued functions [6]. In this paper, we find some operator-valued Bochner integrable functions and prove that the analytic operator-valued function space integral of a certain function is represented as the Bochner integral of operator-valued functions on some conditions.

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RELATIONSHIPS BETWEEN INTEGRAL TRANSFORMS AND CONVOLUTIONS ON AN ANALOGUE OF WIENER SPACE

  • Cho, Dong Hyun
    • Honam Mathematical Journal
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    • v.35 no.1
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    • pp.51-71
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    • 2013
  • In the present paper, we evaluate the analytic conditional Fourier-Feynman transforms and convolution products of unbounded function which is the product of the cylinder function and the function in a Banach algebra which is defined on an analogue o Wiener space and useful in the Feynman integration theories and quantum mechanics. We then investigate the inverse transforms of the function with their relationships and finally prove that th analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions, can be expressed in terms of the product of the conditional Fourier-Feynman transforms of each function.

ON THE ANALYTIC PART OF HARMONIC UNIVALENT FUNCTIONS

  • FRASIN BASEM AREF
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.3
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    • pp.563-569
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    • 2005
  • In [2], Jahangiri studied the harmonic starlike functions of order $\alpha$, and he defined the class T$_{H}$($\alpha$) consisting of functions J = h + $\bar{g}$ where hand g are the analytic and the co-analytic part of the function f, respectively. In this paper, we introduce the class T$_{H}$($\alpha$, $\beta$) of analytic functions and prove various coefficient inequalities, growth and distortion theorems, radius of convexity for the function h, if the function J belongs to the classes T$_{H}$($\alpha$) and T$_{H}$($\alpha$, $\beta$).