Title:
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Increasing sequences of sectorial forms (English) |
Author:
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Vogt, Hendrik |
Author:
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Voigt, Jürgen |
Language:
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English |
Journal:
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Czechoslovak Mathematical Journal |
ISSN:
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0011-4642 (print) |
ISSN:
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1572-9141 (online) |
Volume:
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70 |
Issue:
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4 |
Year:
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2020 |
Pages:
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1033-1046 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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We prove convergence results for `increasing' sequences of sectorial forms. We treat both the case of closed forms and the case of non-closable forms. (English) |
Keyword:
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sectorial form |
Keyword:
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strong resolvent convergence |
MSC:
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47A07 |
idZBL:
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07285977 |
idMR:
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MR4181794 |
DOI:
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10.21136/CMJ.2020.0101-19 |
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Date available:
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2020-11-18T09:45:14Z |
Last updated:
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2023-01-02 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/148409 |
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Reference:
|
[1] Arendt, W.: Approximation of degenerate semigroups.Taiwanese J. Math. 5 (2001), 279-295. Zbl 1025.47023, MR 1832168, 10.11650/twjm/1500407337 |
Reference:
|
[2] Arendt, W., Elst, A. F. M. ter: Sectorial forms and degenerate differential operators.J. Oper. Theory 67 (2012), 33-72. Zbl 1243.47009, MR 2881534 |
Reference:
|
[3] Arendt, W., Nikolski, N.: Vector-valued holomorphic functions revisited.Math. Z. 234 (2000), 777-805. Zbl 0976.46030, MR 1778409, 10.1007/s002090050008 |
Reference:
|
[4] Arens, R.: Operational calculus of linear relations.Pac. J. Math. 11 (1961), 9-23. Zbl 0102.10201, MR 0123188, 10.2140/pjm.1961.11.9 |
Reference:
|
[5] Batty, C. J. K., Elst, A. F. M. ter: On series of sectorial forms.J. Evol. Equ. 14 (2014), 29-47. Zbl 1320.47003, MR 3169030, 10.1007/s00028-013-0205-3 |
Reference:
|
[6] Hassi, S., Sandovici, A., Snoo, H. S. V. de, Winkler, H.: Form sums of nonnegative selfadjoint operators.Acta Math. Hung. 111 (2006), 81-105. Zbl 1122.47011, MR 2188974, 10.1007/s10474-006-0036-6 |
Reference:
|
[7] Kato, T.: Perturbation Theory for Linear Operators.Grundlehren der mathematischen Wissenschaften 132, Springer, Berlin (1966). Zbl 0148.12601, MR 0203473, 10.1007/978-3-662-12678-3_9 |
Reference:
|
[8] Kato, T.: Perturbation Theory for Linear Operators.Grundlehren der mathematischen Wissenschaften 132, Springer, Berlin (1980). Zbl 0435.47001, MR 0203473 |
Reference:
|
[9] Kunze, M.: Form Methods for Linear Evolution Problems on Hilbert Spaces: Diplomarbeit.Fakultät für Mathematik und Wirtschaftswissenschaften, Universität Ulm, Ulm (2005), Available at \brokenlink{https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi. {inst.020/abschlussarbeiten/diplomarbeit_kunze.pdf}}. |
Reference:
|
[10] Ouhabaz, E.-M.: Second order elliptic operators with essential spectrum $[0,\infty)$ on $L^p$.Commun. Partial Differ. Equations 20 (1995), 763-773. Zbl 0869.35065, MR 1326906, 10.1080/03605309508821114 |
Reference:
|
[11] Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations.Applied Mathematical Sciences 44, Springer, New York (1983). Zbl 0516.47023, MR 0710486, 10.1007/978-1-4612-5561-1 |
Reference:
|
[12] Simon, B.: A canonical decomposition for quadratic forms with applications to monotone convergence theorems.J. Funct. Anal. 28 (1978), 377-385. Zbl 0413.47029, MR 0500266, 10.1016/0022-1236(78)90094-0 |
Reference:
|
[13] Vogt, H., Voigt, J.: Holomorphic families of forms, operators and {$C_0$}-semigroups.Monatsh. Math. 187 (2018), 375-380. Zbl 07031542, MR 3850318, 10.1007/s00605-017-1132-0 |
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