Resolvent bounds for jump generators

Kondratiev Y, Molchanov S, Piatnitski A, Zhizhina E (2018)
APPLICABLE ANALYSIS 97(3): 323-336.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Autor*in
Kondratiev, YuriUniBi; Molchanov, Stanislav; Piatnitski, Andrey; Zhizhina, Elena
Abstract / Bemerkung
The paper deals with jump generators with a convolution kernel. Assuming that the kernel decays either exponentially or polynomially, we prove a number of lower and upper bounds for the resolvent of such operators. In particular we focus on sharp estimates of the resolvent kernel for small values of the spectral parameter. We consider two applications of these results. First we obtain pointwise estimates for principal eigenfunction of jump generators perturbed by a compactly supported potential (so-called nonlocal Schrodinger operators). Then we consider the Cauchy problem for the corresponding inhomogeneous evolution equations and study the behaviour of its solutions.
Stichworte
Nonlocal operator; resolvent kernel; dispersal kernel; principal; eigenfunction
Erscheinungsjahr
2018
Zeitschriftentitel
APPLICABLE ANALYSIS
Band
97
Ausgabe
3
Seite(n)
323-336
ISSN
0003-6811
eISSN
1563-504X
Page URI
https://pub.uni-bielefeld.de/record/2918287

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Kondratiev Y, Molchanov S, Piatnitski A, Zhizhina E. Resolvent bounds for jump generators. APPLICABLE ANALYSIS. 2018;97(3):323-336.
Kondratiev, Y., Molchanov, S., Piatnitski, A., & Zhizhina, E. (2018). Resolvent bounds for jump generators. APPLICABLE ANALYSIS, 97(3), 323-336. doi:10.1080/00036811.2016.1263838
Kondratiev, Y., Molchanov, S., Piatnitski, A., and Zhizhina, E. (2018). Resolvent bounds for jump generators. APPLICABLE ANALYSIS 97, 323-336.
Kondratiev, Y., et al., 2018. Resolvent bounds for jump generators. APPLICABLE ANALYSIS, 97(3), p 323-336.
Y. Kondratiev, et al., “Resolvent bounds for jump generators”, APPLICABLE ANALYSIS, vol. 97, 2018, pp. 323-336.
Kondratiev, Y., Molchanov, S., Piatnitski, A., Zhizhina, E.: Resolvent bounds for jump generators. APPLICABLE ANALYSIS. 97, 323-336 (2018).
Kondratiev, Yuri, Molchanov, Stanislav, Piatnitski, Andrey, and Zhizhina, Elena. “Resolvent bounds for jump generators”. APPLICABLE ANALYSIS 97.3 (2018): 323-336.