TITLE:
On the Product of General Differential Operators with Their Point Spectra in the Direct Sum Spaces
AUTHORS:
Sobhy El-Sayed Ibrahim
KEYWORDS:
Product of Quasi-Differential Expressions, Essential Spectra, Joint Field of Regularity, Regularly Solvable Operators, Direct Sum Spaces
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.6,
June
30,
2026
ABSTRACT: In this paper, the product of quasi-differential expressions
τ
1
,
τ
2
,?,
τ
n
each of
nth
order with complex coefficients and its formal adjoints
τ
1
+
,
τ
2
+
,?,
τ
n
+
on any finite number of intervals
I
p
=(
a
p
,
b
p
)
,
p=1,?,N
are considered in the setting of 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 regularity fields of product of differential operators generated by such expressions are obtained. Some of these are extensions or generalizations of those in a symmetric case, and of a general case with one interval case, whilst others are new.