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VERY SLOWLY VARYING FUNCTIONS – II
, 2007
"... This paper is a sequel to both Ash, Erdos and Rubel [AER], on very slowly varying functions, and [BOst1], on foundations of regular variation. We show that generalizations of the AshErdosRubel approach –imposing growth restrictions on the function h, rather than regularity conditions such as measu ..."
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This paper is a sequel to both Ash, Erdos and Rubel [AER], on very slowly varying functions, and [BOst1], on foundations of regular variation. We show that generalizations of the AshErdosRubel approach –imposing growth restrictions on the function h, rather than regularity conditions
GENERAL KERNEL CONVOLUTIONS WITH SLOWLY VARYING FUNCTIONS
"... Abstract. We prove a theorem concerning asymptotic behavior of general complexvalued kernel convolutions with slowly varying functions in the sense of Karamata. In applications we showed that the content of some classical theorems can be naturally extended on some parts of complex zplane. 1. ..."
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Abstract. We prove a theorem concerning asymptotic behavior of general complexvalued kernel convolutions with slowly varying functions in the sense of Karamata. In applications we showed that the content of some classical theorems can be naturally extended on some parts of complex zplane. 1.
ON THE NONCOMMUTATIVE NEUTRIX PRODUCT INVOLVING SLOWLY VARYING FUNCTIONS 1
"... Abstract. Let L(x) be a slowly varying function at both zero and infinity. The existence of the noncommutative neutrix convolution product of the distributions x λ +L(x) and x µ − is proved, where λ, µ are real numbers such that λ, µ / ∈ −N and λ+µ / ∈ −Z. Some other products of distributions are o ..."
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Abstract. Let L(x) be a slowly varying function at both zero and infinity. The existence of the noncommutative neutrix convolution product of the distributions x λ +L(x) and x µ − is proved, where λ, µ are real numbers such that λ, µ / ∈ −N and λ+µ / ∈ −Z. Some other products of distributions
Generalization of Almost Sure Convergence Properties of Pairwise NQD Random Sequences
"... Some sufficient conditions on the almost sure convergence of NQD pairwise random sequences are obtained by using the properties of some slowly varying functions. ..."
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Some sufficient conditions on the almost sure convergence of NQD pairwise random sequences are obtained by using the properties of some slowly varying functions.
all AN ABELTAUBER THEOREM FOR LAPLACE TRANSFORMS
"... An Abelian and Tauberian theorem is proved that is a refinement of Karamata's theorem for slowly varying functions. The theorem is applied to probability distributions. ..."
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An Abelian and Tauberian theorem is proved that is a refinement of Karamata's theorem for slowly varying functions. The theorem is applied to probability distributions.
Auditory perception with slowlyvarying amplitude and frequency modulations
"... natural stimuli, including speech, music, and animal communication sounds. Although amplitude and frequency modulations have been extensively studied physiologically and psychophysically (e.g., Riesz 1928; Grinnell 1963; Suga 1964; ..."
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natural stimuli, including speech, music, and animal communication sounds. Although amplitude and frequency modulations have been extensively studied physiologically and psychophysically (e.g., Riesz 1928; Grinnell 1963; Suga 1964;
G(y)dy (x!1): The corresponding multiplicative form, with
"... Abstract. We relax the continuity assumption in Blooms uniform convergence theorem for Beurling slowly varying functions '. We assume that ' has the Darboux property, and obtain results for ' measurable or having the Baire property. ..."
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Abstract. We relax the continuity assumption in Blooms uniform convergence theorem for Beurling slowly varying functions '. We assume that ' has the Darboux property, and obtain results for ' measurable or having the Baire property.
Beyond Lebesgue and Baire II: bitopology and measurecategory duality
 Colloq. Math
"... We reexamine measurecategory duality by a bitopological approach, using both the Euclidean and the density topologies of the line. We give a topological result (on convergence of homeomorphisms to the identity) obtaining as a corollary results on infinitary combinatorics due to Kestelman and to Bo ..."
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Cited by 12 (9 self)
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and to Borwein and Ditor. We hence give a unified proof of the measure and category cases of Uniform Convergence Theorem for slowly varying functions. We also extend results on very slowly varying functions of Ash, Erdős and Rubel.
GOOD DECOMPOSITION IN THE CLASS OF CONVEX FUNCTIONS OF HIGHER ORDER
"... Abstract. The problems investigated in this article are connected to the fact that the class of slowly varying functions is not closed with respect to the operation of subtraction. We study the class of functions Fk−1, which are nonnegative and iconvex for 0 i < k, where k is a positive integer ..."
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Abstract. The problems investigated in this article are connected to the fact that the class of slowly varying functions is not closed with respect to the operation of subtraction. We study the class of functions Fk−1, which are nonnegative and iconvex for 0 i < k, where k is a positive
Results 1  10
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428,648