The spectra of general differential operators in the direct sum spaces

Sobhy El-sayed Ibrahim

Czechoslovak Mathematical Journal (2004)

  • Volume: 54, Issue: 1, page 9-29
  • ISSN: 0011-4642

Abstract

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In this paper, the general ordinary quasi-differential expression M p of n -th order with complex coefficients and its formal adjoint M p + on any finite number of intervals I p = ( a p , b p ) , p = 1 , ⋯ , N , are considered in the setting of the direct sums of L w p 2 ( a p , b p ) -spaces of functions defined on each of the separate intervals, and a number of results concerning the location of the point spectra and the regularity fields of general differential operators generated by such expressions are obtained. Some of these are extensions or generalizations of those in a symmetric case in [1], [14], [15], [16], [17] and of a general case with one interval in [2], [11], [12], whilst others are new.

How to cite

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Ibrahim, Sobhy El-sayed. "The spectra of general differential operators in the direct sum spaces." Czechoslovak Mathematical Journal 54.1 (2004): 9-29. <http://eudml.org/doc/30835>.

@article{Ibrahim2004,
abstract = {In this paper, the general ordinary quasi-differential expression $M_p$ of $n$-th order with complex coefficients and its formal adjoint $M_p^+$ on any finite number of intervals $I_p=(a_p,b_p)$, $p=1,\dots ,N$, are considered in the setting of the direct sums of $L_\{w_p\}^2(a_p,b_p)$-spaces of functions defined on each of the separate intervals, and a number of results concerning the location of the point spectra and the regularity fields of general differential operators generated by such expressions are obtained. Some of these are extensions or generalizations of those in a symmetric case in [1], [14], [15], [16], [17] and of a general case with one interval in [2], [11], [12], whilst others are new.},
author = {Ibrahim, Sobhy El-sayed},
journal = {Czechoslovak Mathematical Journal},
keywords = {quasi-differential expressions; essential spectra; joint field of regularity; regularly solvable operators; direct sum spaces; quasi-differential expressions; essential spectra; joint field of regularity; regularly solvable operators; direct sum spaces},
language = {eng},
number = {1},
pages = {9-29},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The spectra of general differential operators in the direct sum spaces},
url = {http://eudml.org/doc/30835},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Ibrahim, Sobhy El-sayed
TI - The spectra of general differential operators in the direct sum spaces
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 1
SP - 9
EP - 29
AB - In this paper, the general ordinary quasi-differential expression $M_p$ of $n$-th order with complex coefficients and its formal adjoint $M_p^+$ on any finite number of intervals $I_p=(a_p,b_p)$, $p=1,\dots ,N$, are considered in the setting of the direct sums of $L_{w_p}^2(a_p,b_p)$-spaces of functions defined on each of the separate intervals, and a number of results concerning the location of the point spectra and the regularity fields of general differential operators generated by such expressions are obtained. Some of these are extensions or generalizations of those in a symmetric case in [1], [14], [15], [16], [17] and of a general case with one interval in [2], [11], [12], whilst others are new.
LA - eng
KW - quasi-differential expressions; essential spectra; joint field of regularity; regularly solvable operators; direct sum spaces; quasi-differential expressions; essential spectra; joint field of regularity; regularly solvable operators; direct sum spaces
UR - http://eudml.org/doc/30835
ER -

References

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  16. On the essential spectra of linear 2 n -th order differential operators with complex coefficients, Proc. Roy. Soc. Edinburgh 92 (1982), 65–75. (1982) MR0667125
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