A characterization of holomorphic bivariate functions of bounded index
-
Richard F. Patterson
and
Fatih Nuray
Abstract
The following notion of bounded index for complex entire functions was presented by Lepson. function f(z) is of bounded index if there exists an integer N independent of z, such that
The main goal of this paper is extend this notion to holomorphic bivariate function. To that end, we obtain the following definition. A holomorphic bivariate function is of bounded index, if there exist two integers M and N such that M and N are the least integers such that
Using this notion we present necessary and sufficient conditions that ensure that a holomorphic bivariate function is of bounded index.
References
[1] Fricke, G. H.: A characterization of functions of bounded index, Indian J. Math. 14 (1972), 207–212.Search in Google Scholar
[2] Hamilton, H. J.: Transformations of multiple sequences, Duke Math. J. 2 (1936), 29–60.10.1215/S0012-7094-36-00204-1Search in Google Scholar
[3] Hardy, G. H.: Divergent Series, Oxford University Press, 1949.Search in Google Scholar
[4] Lepson, B.: Differential equations of infinite order, hyperdirichlet series and entire functions of bounded index. Lecture Notes, 1966, Summer Institute on Entire Functions, Univ. of California, La Jolla, California.Search in Google Scholar
[5] Patterson, R. F.: Analogues of some fundamental theorems of summability theory, Int. J. Math. Math. Sci. 23, (2000), 1-9.10.1155/S0161171200001782Search in Google Scholar
[6] Pringsheim, A.: Zür Theorie der zweifach unendlichen Zahlenfolgen, Math. Ann. 53 (1900), 289–321.10.1007/BF01448977Search in Google Scholar
[7] Robison, G. M.: Divergent double sequences and series, Amer. Math. Soc. Trans. 28 (1926), 50–73.10.1090/S0002-9947-1926-1501332-5Search in Google Scholar
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Articles in the same Issue
- Some results in local Hilbert algebras
- A note on residuated po-groupoids and lattices with antitone involutions
- The first law of cubology for the Rubik’s Revenge
- Conditional associativity in orthomodular lattices
- A monotonicity property for generalized Fibonacci sequences
- Systems of conditionally independent sets
- On the k-th order lfsr sequence with public key cryptosystems
- On parametric spaces of bicentric quadrilaterals
- Character sums with an explicit evaluation
- Some remarks on formal power series and formal Laurent series
- The co-rank of the fundamental group: The direct product, the first Betti number, and the topology of foliations
- On prime and semiprime generalized hyperaction of hypermonoid
- On O’Malley ϱ-upper continuous functions
- Uniqueness theorems for finitely additive probabilities on quantum structures
- Some results on differential-difference analogues of Brück conjecture
- Oscillation of neutral second order half-linear differential equations without commutativity in deviating arguments
- On support, separation and decomposition theorems for t-Wright-concave functions
- A characterization of holomorphic bivariate functions of bounded index
- Asymptotic expansion of double Laplace-type integrals with a curve of minimal points and application to an exit time problem
- The geometry of two-valued subsets of Lp-spaces
- Hemi-slant submanifolds as warped products in a nearly Kaehler manifold
- A comparison of two tests in multivariate models
- Modelling prescription behaviour of general practitioners
- Characterization of congruence lattices of principal p-algebras
