Qarayev R., Mammedzadeh G. S.
MATHEMATICA SLOVACA, vol.75, no.6, pp.1453-1460, 2025 (SCI-Expanded, Scopus)
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Publication Type:
Article / Article
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Volume:
75
Issue:
6
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Publication Date:
2025
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Doi Number:
10.1515/ms-2025-0106
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Journal Name:
MATHEMATICA SLOVACA
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Journal Indexes:
Scopus, Science Citation Index Expanded (SCI-EXPANDED), MathSciNet, zbMATH
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Page Numbers:
pp.1453-1460
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Open Archive Collection:
Article
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Azerbaijan State University of Economics (UNEC) Affiliated:
Yes
Abstract
Abstract
We consider the classical double convolution product and the Duhamel product for functions in two variables and study their some properties and applications. Namely, we investigate *-generators of the Banach algebra
C
x
y
(
n
)
:=
f
∈
C
n
t
[
0
,
1
]
×
t
[
0
,
1
]
:
f
(
x
,
y
)
=
g
(
x
y
)
for some
g
∈
C
t
[
0
,
1
]
(
n
)
.
$$C^{(n)}_{xy}:=\left\{f\in C^{n}\left(t[0,1]\times t[0,1]\right) :f(x,y)=g(xy)\,\,\text{for some}\,\,g\in C^{(n)}_{t[0,1]}\right\} .
$$
Also we describe the maximal ideal space of the Banach algebra
(
C
x
y
(
n
)
,
⊛
)
$ (C^{(n)}_{xy},\circledast) $
with respect to the Duhamel product ⊛ defined by
(
f
⊛
g
)
(
x
,
y
)
=
∂
2
∂
x
∂
y
∫
0
x
∫
0
y
f
(
x
−
t
)
(
y
−
τ
)
g
(
t
τ
)
d
τ
d
t
.
$$(f\circledast g)(x,y)=\frac{\partial^{2}}{\partial x\partial y} \int \limits_{0}^{x}\int \limits_{0}^{y} f(x-t)(y-\tau)g(t\tau)\text{d}\tau\, {\text{d}} t.
$$