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Full-Text Articles in Physical Sciences and Mathematics
On Weighted Integrability Of Trigonometric Series And L¹-Convergence Of Fourier Series, William O. Bray, Caslav V. Stanojević
On Weighted Integrability Of Trigonometric Series And L¹-Convergence Of Fourier Series, William O. Bray, Caslav V. Stanojević
Mathematics and Statistics Faculty Research & Creative Works
Result concerning integrability of f(x)L(l/x)(g(x)L(l/x)), where f(x)(g(x)) is the pointwise limit of certain cosine (sine) series and L(•) is slowly vary in the sense of Karamata [5] is proved. Our result is an excludedďcase in more classical results (see [4]) and also generalizes a result of G. A. Fomin [1]. Also a result of Fomin and Telyakovskii [6] concerning L1-convergence of Fourier series is generalized. Both theorems make use of a generalized notion of quasi-monotone sequences. © 1986 American Mathematical Society.
Banach Spaces Of Functions Analytic In A Polydisc, Leon M. Hall
Banach Spaces Of Functions Analytic In A Polydisc, Leon M. Hall
Mathematics and Statistics Faculty Research & Creative Works
This paper is concerned with functions of several complex variables analytic in the unit polydisc. Certain Banach spaces to which these functions might belong are defined and some relationships between them are developed. The space of linear functionals for the Banach space of functions analytic in the open unit polydisc and continuous on the unit torus is then described in terms of analytic functions using an extension of the Hadamard product.
On The Mean Time Between Failures For Repairable Systems, Max Engelhardt, Lee J. Bain
On The Mean Time Between Failures For Repairable Systems, Max Engelhardt, Lee J. Bain
Geosciences and Geological and Petroleum Engineering Faculty Research & Creative Works
Much of the recent work on modeling repairable systems involves Poisson processes with nonconstant intensity functions, viz, nonhomogeneous Poisson processes. Since times between failures are not identically distributed when the process is nonhomogeneous, it is not clear what concept should take the place of the mean time between failures in assessing the reliability of a repairable system. A number of alternate concepts can be found in the literature. We investigate the relationship between two of the most frequently considered alternatives: the reciprocal of the intensity function, and the mean waiting time from t until the next failure. Theorem 1 states …