Displaying similar documents to “Resolvent conditions and powers of operators”

On the growth of the resolvent operators for power bounded operators

Olavi Nevanlinna (1997)

Banach Center Publications

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Outline. In this paper I discuss some quantitative aspects related to power bounded operators T and to the decay of T n ( T - 1 ) . For background I refer to two recent surveys J. Zemánek [1994], C. J. K. Batty [1994]. Here I try to complement these two surveys in two different directions. First, if the decay of T n ( T - 1 ) is as fast as O(1/n) then quite strong conclusions can be made. The situation can be thought of as a discrete version of analytic semigroups; I try to motivate this in Section 1 by demonstrating...

On the growth of an algebroid function with radially distributed values

Nan Wu, Jian Hua Zheng (2015)

Annales Polonici Mathematici

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We investigate how the growth of an algebroid function could be affected by the distribution of the arguments of its a-points in the complex plane. We give estimates of the growth order of an algebroid function with radially distributed values, which are counterparts of results for meromorphic functions with radially distributed values.

Comparative growth analysis of Wronskians in the light of their relative orders

Sanjib Kumar Datta, Tanmay Biswas, Ahsanul Hoque (2015)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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In this paper we study the comparative growth properties of a composition of entire and meromorphic functions on the basis of the relative order (relative lower order) of Wronskians generated by entire and meromorphic functions.

Growth of (frequently) hypercyclic functions for differential operators

Hans-Peter Beise, Jürgen Müller (2011)

Studia Mathematica

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We investigate the conjugate indicator diagram or, equivalently, the indicator function of (frequently) hypercyclic functions of exponential type for differential operators. This gives insights into growth conditions for these functions on particular rays or sectors. Our research extends known results in several respects.

Hyper-order and order of meromorphic functions sharing functions

Jianming Qi, Wenjun Yuan, Hongxun Yi (2015)

Annales Polonici Mathematici

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In this paper we mainly estimate the hyper-order of an entire function which shares one function with its derivatives. Some examples are given to show that the conclusions are meaningful.

Polaroid type operators and compact perturbations

Chun Guang Li, Ting Ting Zhou (2014)

Studia Mathematica

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A bounded linear operator T acting on a Hilbert space is said to be polaroid if each isolated point in the spectrum is a pole of the resolvent of T. There are several generalizations of the polaroid property. We investigate compact perturbations of polaroid type operators. We prove that, given an operator T and ε > 0, there exists a compact operator K with ||K|| < ε such that T + K is polaroid. Moreover, we characterize those operators for which a certain polaroid type property...

On meromorphic solutions of the Riccati differential equations

Ran Ran Zhang, Zong Xuan Chen (2010)

Annales Polonici Mathematici

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We investigate the growth and Borel exceptional values of meromorphic solutions of the Riccati differential equation w' = a(z) + b(z)w + w², where a(z) and b(z) are meromorphic functions. In particular, we correct a result of E. Hille [Ordinary Differential Equations in the Complex Domain, 1976] and get a precise estimate on the growth order of the transcendental meromorphic solution w(z); and if at least one of a(z) and b(z) is non-constant, then we...

Restricted interpolation by meromorphic inner functions

Alexei Poltoratski, Rishika Rupam (2016)

Concrete Operators

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Meromorphic Inner Functions (MIFs) on the upper half plane play an important role in applications to spectral problems for differential operators. In this paper, we survey some recent results concerning function theoretic properties of MIFs and show their connections with spectral problems for the Schrödinger operator.

Another algebraic proof of Weil's reciprocity

Emma Previato (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The Burchnall-Chaundy-Krichever correspondence which converts meromorphic functions on a curve into differential operators is used to interpret Weil's reciprocity as the calculation of a resultant.

Further investigations on a question of Zhang and Lü

Abhijit Banerjee, Bikash Chakraborty (2015)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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In the paper based on the question of Zhang and Lü [15], we present one theorem which will improve and extend results of Banerjee-Majumder [2] and a recent result of Li-Huang [9].

Selected results of the theory of value distribution and growth of meromorphic functions

Ewa Ciechanowicz (2015)

Banach Center Publications

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The paper discusses development of the theory of value distribution and growth of meromorphic functions, focusing on two basic notions: exceptional values and asymptotic values. Some historical context is given and contemporary achievements are presented. In particular, recent results concerning exceptional functions and asymptotic functions are considered.