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Silvestru Sever Dragomir (2015)
Open Mathematics
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We establish in this paper some Jensen’s type inequalities for functions defined by power series with nonnegative coefficients. Applications for functions of selfadjoint operators on complex Hilbert spaces are provided as well.
Heydar Radjavi, Ping-Kwan Tam, Kok-Keong Tan (2003)
Studia Mathematica
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A mean ergodic theorem is proved for a compact operator on a Banach space without assuming mean-boundedness. Some related results are also presented.
Józef Siciak (2011)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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We study extensions of classical theorems on gap power series of a complex variable to the multidimensional case.
Józef Siciak (2011)
Annales UMCS, Mathematica
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We study extensions of classical theorems on gap power series of a complex variable to the multidimensional case.
Dragoš M. Cvetković (1972)
Publications de l'Institut Mathématique
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M. S. Popadić (1970)
Matematički Vesnik
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Andrzej Birkholc (1971)
Colloquium Mathematicae
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Lev Aizenberg (2007)
Studia Mathematica
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The Bohr radius for power series of holomorphic functions mapping Reinhardt domains 𝓓 ⊂ ℂⁿ into a convex domain G ⊂ ℂ is independent of the domain G.
Takeshi Yoshimoto (1982)
Studia Mathematica
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Árpád Baricz, Jetro Vesti, Matti Vuorinen (2011)
Annales UMCS, Mathematica
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T. Kaluza has given a criterion for the signs of the power series of a function that is the reciprocal of another power series. In this note the sharpness of this condition is explored and various examples in terms of the Gaussian hypergeometric series are given. A criterion for the monotonicity of the quotient of two power series due to M. Biernacki and J. Krzyż is applied.
Arpad Baricz, Jetro Vesti, Matti Vuorinen (2011)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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T. Kaluza has given a criterion for the signs of the power series of a function that is the reciprocal of another power series. In this note the sharpness of this condition is explored and various examples in terms of the Gaussian hypergeometric series are given. A criterion for the monotonicity of the quotient of two power series due to M. Biernacki and J. Krzyż is applied.
Karol Borsuk (1972)
Colloquium Mathematicae
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Teresa Bermúdez, Manuel González, Mostafa Mbekhta (2000)
Studia Mathematica
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We prove that if some power of an operator is ergodic, then the operator itself is ergodic. The converse is not true.
Babu Ram (1974)
Colloquium Mathematicae
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Wenguang Zhai (2004)
Acta Arithmetica
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Xiao-Xiong Gan, Dariusz Bugajewski (2010)
Commentationes Mathematicae Universitatis Carolinae
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In this note we investigate a relationship between the boundary behavior of power series and the composition of formal power series. In particular, we prove that the composition domain of a formal power series is convex and balanced which implies that the subset consisting of formal power series which can be composed by a formal power series possesses such properties. We also provide a necessary and sufficient condition for the superposition operator to map into itself or to...
Ryszard Rębowski (1987)
Colloquium Mathematicae
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Lasha Ephremidze (2003)
Studia Mathematica
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The Stein-Weiss theorem that the distribution function of the Hilbert transform of the characteristic function of E depends only on the measure of E is generalized to the ergodic Hilbert transform.
Ping Kwan Tam, Kok-Keong Tan (2002)
Studia Mathematica
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The notion of local mean ergodicity is introduced. Some general locally mean ergodic theorems for linear and affine operators are presented. Locally mean ergodic theorems for affine operators whose linear parts are compact or similar to subnormal operators on a Hilbert space are given.