On Convergence of Series of Simple Partial Fractions in L p ℝ $$ Lp\left(\mathrm{\mathbb{R}}\right) $$
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| 024 | 7 | 0 | |a 10.1007/s10958-015-2583-2 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10958-015-2583-2 | ||
| 100 | 1 | |a Dodonov |D A. |u A. G. and N. G. Stoletov Vladimir State University, 87, Gor'kogo St., 600000, Vladimir, Russia |4 aut | |
| 245 | 1 | 0 | |a On Convergence of Series of Simple Partial Fractions in L p ℝ $$ Lp\left(\mathrm{\mathbb{R}}\right) $$ |h [Elektronische Daten] |c [A. Dodonov] |
| 520 | 3 | |a We show that the necessary condition for the convergence of the series of simple partial fractions ∑ k = 1 ∞ z − z k − 1 $$ {\displaystyle \sum_{k=1}^{\infty }{\left(z-{z}_k\right)}^{-1}} $$ in L p ℝ $$ Lp\left(\mathrm{\mathbb{R}}\right) $$ , 1 < p < ∞, is the convergence of the series ∑ k = 1 ∞ z k − 1 / q 1 n − 1 − ε z k + 1 $$ {\displaystyle \sum_{k=1}^{\infty }{\left|{z}_k\right|}^{-1/q}1{\mathrm{n}}^{-1-\varepsilon}\left(\left|{z}_k\right|+1\right)} $$ , ε > 0. In the case 1 < p < 2, we obtain a convergence criterion in terms of the imaginary parts of poles under the condition that all the poles z k = x k + iy k belong to the angle |z k | ≤ α|y k | with a fixed α > 0. | |
| 540 | |a Springer Science+Business Media New York, 2015 | ||
| 773 | 0 | |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 210/5(2015-11-01), 648-653 |x 1072-3374 |q 210:5<648 |1 2015 |2 210 |o 10958 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10958-015-2583-2 |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/s10958-015-2583-2 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Dodonov |D A. |u A. G. and N. G. Stoletov Vladimir State University, 87, Gor'kogo St., 600000, Vladimir, Russia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 210/5(2015-11-01), 648-653 |x 1072-3374 |q 210:5<648 |1 2015 |2 210 |o 10958 | ||