On a functional equation appearing in characterization of distributions by the optimality of an estimate
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| 008 | 210128e20150601xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00010-014-0254-x |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-014-0254-x | ||
| 245 | 0 | 0 | |a On a functional equation appearing in characterization of distributions by the optimality of an estimate |h [Elektronische Daten] |c [Gennadiy Feldman, Piotr Graczyk] |
| 520 | 3 | |a Let X be a second countable locally compact Abelian group containing no subgroup topologically isomorphic to the circle group $${\mathbb{T}}$$ T , Y be its character group. Letμ be a probability distribution on X such that its characteristic function $${\widehat\mu(y)}$$ μ ^ ( y ) does not vanish and $${\widehat\mu(y)}$$ μ ^ ( y ) for some $${n \geq 3}$$ n ≥ 3 satisfies the equation $$\prod_{j=1}^{n} \hat\mu(y_j + y) = \prod_{j=1}^{n}\hat\mu(y_j - y), \quad \sum_{j=1}^{n} y_j = 0, \quad y_1,\dots,y_n,y \in Y.$$ ∏ j = 1 n μ ^ ( y j + y ) = ∏ j = 1 n μ ^ ( y j - y ) , ∑ j = 1 n y j = 0 , y 1 , ⋯ , y n , y ∈ Y . Thenμ is a convolution of a Gaussian distribution and a distribution supported in the subgroup of X generated by elements of order 2. | |
| 540 | |a Springer Basel, 2014 | ||
| 690 | 7 | |a Difference equation |2 nationallicence | |
| 690 | 7 | |a Gaussian distribution |2 nationallicence | |
| 690 | 7 | |a optimal estimate |2 nationallicence | |
| 700 | 1 | |a Feldman |D Gennadiy |u B. Verkin Institute for Low Temperature, Physics and Engineering, 47, Lenin ave, 61103, Kharkiv, Ukraine |4 aut | |
| 700 | 1 | |a Graczyk |D Piotr |u Laboratoire LAREMA UMR 6093-CNRS, Universite a'Angers, 2 bd. Lavoisier, 49045, Angers, France |4 aut | |
| 773 | 0 | |t Aequationes mathematicae |d Springer Basel |g 89/3(2015-06-01), 663-671 |x 0001-9054 |q 89:3<663 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-014-0254-x |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00010-014-0254-x |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Feldman |D Gennadiy |u B. Verkin Institute for Low Temperature, Physics and Engineering, 47, Lenin ave, 61103, Kharkiv, Ukraine |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Graczyk |D Piotr |u Laboratoire LAREMA UMR 6093-CNRS, Universite a'Angers, 2 bd. Lavoisier, 49045, Angers, France |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer Basel |g 89/3(2015-06-01), 663-671 |x 0001-9054 |q 89:3<663 |1 2015 |2 89 |o 10 | ||