Beurling regular variation, Bloom dichotomy, and the Gołąb-Schinzel functional equation
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| 024 | 7 | 0 | |a 10.1007/s00010-014-0260-z |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-014-0260-z | ||
| 100 | 1 | |a Ostaszewski |D A. |u Mathematics Department, London School of Economics, Houghton Street, WC2A 2AE, London, UK |4 aut | |
| 245 | 1 | 0 | |a Beurling regular variation, Bloom dichotomy, and the Gołąb-Schinzel functional equation |h [Elektronische Daten] |c [A. Ostaszewski] |
| 520 | 3 | |a The class of ‘self-neglecting' functions at the heart of Beurling slow variation is expanded by permitting a positive asymptotic limit function λ(t), in place of the usual limit 1, necessarily satisfying the following ‘self-neglect' condition: $$\lambda (x)\lambda (y) = \lambda (x + y\lambda (x)),$$ λ ( x ) λ ( y ) = λ ( x + y λ ( x ) ) , known as the Gołąb-Schinzel functional equation, a relative of the Cauchy equation (which is itself also central to Karamata regular variation). This equation, due independently to Aczél and Gołąb, occurring in the study of one-parameter subgroups, is here accessory to the λ -Uniform Convergence Theorem (λ-UCT) for the recent, flow-motivated, ‘Beurling regular variation'. Positive solutions, when continuous, are known to be λ(t) = 1+at (below a new, ‘flow', proof is given); a = 0 recovers the usual limit 1 for self-neglecting functions. The λ-UCT allows the inclusion of Karamata multiplicative regular variation in the Beurling theory of regular variation, with λ (t) = 1+t being the relevant case here, and generalizes Bloom's theorem concerning self-neglecting functions. | |
| 540 | |a Springer Basel, 2014 | ||
| 690 | 7 | |a Beurling regular variation |2 nationallicence | |
| 690 | 7 | |a Beurling's equation |2 nationallicence | |
| 690 | 7 | |a self-neglecting functions |2 nationallicence | |
| 690 | 7 | |a uniform convergence theorem |2 nationallicence | |
| 690 | 7 | |a category-measure duality |2 nationallicence | |
| 690 | 7 | |a Bloom dichotomy |2 nationallicence | |
| 690 | 7 | |a Gołąb-Schinzel functional equation |2 nationallicence | |
| 773 | 0 | |t Aequationes mathematicae |d Springer Basel |g 89/3(2015-06-01), 725-744 |x 0001-9054 |q 89:3<725 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-014-0260-z |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/s00010-014-0260-z |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Ostaszewski |D A. |u Mathematics Department, London School of Economics, Houghton Street, WC2A 2AE, London, UK |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer Basel |g 89/3(2015-06-01), 725-744 |x 0001-9054 |q 89:3<725 |1 2015 |2 89 |o 10 | ||