• Kyungpook Mathematical Journal
• /
• 제64권2호
• /
• pp.219-233
• /
• 2024

In this paper, we study the generalized Fourier-Feynman transform (GFFT) for functions on the general Wiener space C_a,b[0, T]. We establish an explicit evaluation formula for the analytic GFFT of bounded cylinder functions on C_a,b[0, T]. We start by examining certain cylinder functions which belong in a Banach algebra of bounded functions on C_a,b[0, T]. We then obtain an explicit formula for the analytic GFFT of the bounded cylinder functions.

• 호남수학학술지
• /
• 제23권1호
• /
• pp.29-39
• /
• 2001

Let $\mathcal{B}$ be a Banach space of analytic functions defined on the open unit disk. Assume S is a bounded operator defined on $\mathcal{B}$ such that S is in the commutant of $M_zn$ or $SM_zn=-M_znS$ for some positive integer n. We give necessary and sufficient condition between compactness of $SM_z+cM_zS$ where c = 1, -1, i, -i, and the structure of S. Also we characterize the commutant of $M_zn$ for some positive integer n.

• Kyungpook Mathematical Journal
• /
• 제60권1호
• /
• pp.127-132
• /
• 2020

In this article, we determine sufficient conditions on the parameters of a generalized convolution operator to ensure that it belongs to the Hardy space and to the space of bounded analytic functions. We exhibit the utility of these results by deducing several interesting examples.

• 대한수학회보
• /
• 제35권2호
• /
• pp.293-299
• /
• 1998

In this note we consider some characterizations of analytic functions of bounded and vanishing mean oscillation on the unit disk in $\mathbb{C}$ and answer a question about them in the negative.

• Korean Journal of Mathematics
• /
• 제29권2호
• /
• pp.293-304
• /
• 2021

In this paper, we present a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions. For new inequalities, the results of Rogosinski's lemma, Subordination principle and Jack's lemma were used.

• 대한수학회보
• /
• 제44권4호
• /
• pp.683-689
• /
• 2007

Let $\mathcal{B}$ be a certain Banach space consisting of analytic functions defined on a bounded domain G in the complex plane. Let ${\varphi}$ be an analytic polynomial or a rational function and let $M_{\varphi}$ denote the operator of multiplication by ${\varphi}$. Under certain condition on ${\varphi}$ and G, we characterize the commutant of $M_{\varphi}$ that is the set of all bounded operators T such that $TM_{\varphi}=M_{\varphi}T$. We show that $T=M_{\Psi}$, for some function ${\Psi}$ in $\mathcal{B}$.

• Korean Journal of Mathematics
• /
• 제27권4호
• /
• pp.1027-1041
• /
• 2019

In this paper, we present a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions. For new inequalities, the results of Jack's lemma and Hankel determinant were used. We will get a sharp upper bound for Hankel determinant H₂(1). Also, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained.

• 호남수학학술지
• /
• 제17권1호
• /
• pp.97-106
• /
• 1995

We introduce a new class of analytic functions in the unit disk which generalizes the concepts of close-to-convexity and of bounded boundary rotation, and study its various properties including its connection with other classes of analytic and univalent functions.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제28권3호
• /
• pp.235-246
• /
• 2021

In this study, a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions, is considered.The results of Rogosinskis lemma and Jacks lemma have been utilized to derive novel inequalities. Also, these inequalities have been strengthened by considering the critical points which are different from zero.

• 대한수학회보
• /
• 제52권1호
• /
• pp.85-103
• /
• 2015

We prove some sharp extremal distance results for functions in various spaces of analytic functions on bounded strictly pseudoconvex domains with smooth boundary. Also, we obtain atomic decompositions in multifunctional Bloch and weighted Bergman spaces of analytic functions on strictly pseudoconvex domains with smooth boundary, which extend known results in the classical case of a single function.