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Products of Distributions: Nonstandard Methods
Zeitschrift für Analysis und ihre Anwendungen, 1988Nonstandard tools are developed which are suitable for studying products of distributions defined by regularization and passage to the limit. We obtain nonstandard criteria for the existence of the products (which are demonstrated to be useful for calculating standard examples) as well as new standard results clarifying the relationship between ...
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VALUE DISTRIBUTION OF INTERPOLATING BLASCHKE PRODUCTS
Journal of the London Mathematical Society, 2005Given an inner function \(u\) and a complex number \(a\in\mathbb D\), the function \(u_a:=(a-u)(1-\overline a u)^{-1}\) is called the Frostamn shift of \(u\). The celebrated Frostman's theorem claims that \(u_a\) is a Blaschke product unless \(a\) belongs to some exceptional set \(E(u)\) of logarithmic capacity zero. McLaughlin and Piranian showed that
Gorkin, Pamela, Mortini, Raymond
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Angular Distribution of Radioactive Disintegration Products
Nature, 1948THE thermodynamics of the orientation of nuclei by strong magnetic fields at very low temperatures was worked out by Simon1 in 1939. He found that with fields of 100,000 gauss and temperatures of 0·01° K., that is, under conditions which can be realized experimentally, the entropy of nuclear spin systems should be decreased by about 20–30 per cent, and
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Product representations of teletherapy dose distributions
Medical Physics, 1983Product representations are frequently used for teletherapy dose distributions. For example, the dose in a central plane is often written as the product of two factors, one dependent on the depth and the other on the transverse variable. We have answered the following question: given a (two‐dimensional) set of data, how closely is it possible to ...
D, Jette +4 more
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Distribution of Autoxidation Products
1981I discuss in this chapter the distribution of cholesterol autoxidation products in Nature and also of their natural occurrence as reported over the years by other investigators. The term “natural occurrence” should pose no difficulties if we retain the obvious meaning of occurrence in Nature, the term conveying no implication of enzymic derivation ...
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Distribution of products of independently distributed pathway random variables
Statistics, 2013A lot of work has been done on products and ratios of random variables by Provost and his co-workers, see, for example, Provost [S.B. Provost, The exact distribution of the ratio of a linear combination of chi-square variables over the root of a product of chi-square variables, Canad. J. Statist. 14 (1986), pp. 61–67; S.B.
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Distributed planning of collaborative production
The International Journal of Advanced Manufacturing Technology, 1993Collaborative production is viewed in two related dimensions: collaboration among machines to achieve increased reliability, quality and productivity; and collaboration between machines and human supervisors to combine internal and global control information.
Ray E. Eberts, Shimon Y. Nof
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1988
In this paper we prove the inequality by which the Fourier transform of the product |x|r s(x) for s ∈ S(ℝn), x ∈ ℝn, r > 0, is estimated. The product \({\left| {\text{x}} \right|^{\text{r}}}\cdot\mathop f\limits^ \wedge\) is also defined, where f is a real locally integrable function on ℝn and \(\mathop f\limits^ \wedge\) it is the Fourier transforms ...
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In this paper we prove the inequality by which the Fourier transform of the product |x|r s(x) for s ∈ S(ℝn), x ∈ ℝn, r > 0, is estimated. The product \({\left| {\text{x}} \right|^{\text{r}}}\cdot\mathop f\limits^ \wedge\) is also defined, where f is a real locally integrable function on ℝn and \(\mathop f\limits^ \wedge\) it is the Fourier transforms ...
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The Direct Product of Distributions
2021In this chapter we define the direct product of two distributions and we prove that it is well defined. In the chapter are proved the commutativity and associativity of the direct product of distributions. They are considered some applications of the direct product of distributions.
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Some Colombeau products of distributions
1997Summary: By ``Colombeau product of distributions'' we mean the product of some distributions, as they are embedded in Colombeau algebra \(\mathfrak{G}({\mathbb{R}}^m)\), whenever the result can be evaluated in terms of distributions again. Here we propose some results on Colombeau product of the distributions \(x_{\pm}^a\) and \(\delta^{(p)}(x)\), \(x\)
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