The solutions of then-dimensional Bessel diamond operator and the Fourier-Bessel transform of their convolution

Yıldırım, Hüseyin; Sarıkaya, Mehmet Zeki; Öztürk, Sermin

doi:10.1007/bf02829442

Cited by 27 publications

(11 citation statements)

References 4 publications

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“…Let S α (x) and R β (x) be defined by (4) and (5) respectively. Then S α (x) * R β (x) exists and it is a tempered distribution.…”

Section: Lemma 26mentioning

confidence: 99%

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The compound equation related to the Bessel-Helmholtz equation and the Bessel-Klein-Gordon equation

Bunpog¹

2013

ams

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In this paper we study the compound equation N i=1 M j=1 (B + a 2) i (2 B + b 2) j u(x) = f (x), (1) where x = (x 1 , x 2 ,. .. , x n) ∈ R n + = {x ∈ R n | x i > 0}, a and b are nonzero constants. u(x) is unknown function and f (x) is a given distribution. (B + a 2) i is the Bessel-Helmholtz operator iterated i−times and (2 B + b 2) j is the Bessel-Klein-Gordon operator iterated j−times. The existence and the uniqueness solution of (1) is proven.

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“…Let S α (x) and R β (x) be defined by (4) and (5) respectively. Then S α (x) * R β (x) exists and it is a tempered distribution.…”

Section: Lemma 26mentioning

confidence: 99%

“…Later, Hüseyin Yildirim, Mzeki Sarikaya and SerminÖztürk [5] introduce the Bessel diamond operator ♦ k B iterated k−times, defined by…”

Section: Introductionmentioning

confidence: 99%

The compound equation related to the Bessel-Helmholtz equation and the Bessel-Klein-Gordon equation

Bunpog¹

2013

ams

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“…Yildirim, Sarikaya and Ozturk [7] have showed that (−1) t S 2t (a) * R 2t (a) is the solution of the ♦ t B (−1) t S 2t (a) * R 2t (a) = δ , where…”

Section: Introductionmentioning

confidence: 99%

On the Bessel Operator $\odot_{B}^{t}$ Related to the Bessel-Helmholtz and Bessel Klein-Gordon Operator

Bupasiri

2018

Eur. J. Pure Appl. Math.

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In this paper, we study the Bessel operator $\odot_{B}^{t}$, iterated $t$-times and denote by $$\odot_{B}^{t}= \left(\left(B_{a_{1}}+\cdots+B_{a_{p}}+m^{2}\right)^{2} - \left(B_{a_{p+1}}+\cdots+B_{a_{p+q}}\right)^{2}\right)^{t} \nonumber\\$$where $p+q=n, B_{a_i}=\frac{\partial^2}{\partial a_{i}^2}+\frac{2v_i}{a_i}\frac{\partial}{\partial a_{i}}, 2v_i=2\alpha_i+1, \alpha_i>-\frac{1}{2}, a_i>0$, $t\in \mathbb{Z}^+ \cup \{0\}$, $m\in \mathbb{R}^+ \cup \{0\}$ and $p+q=n$ is the dimension of $\mathbb{R}_{n}^{+}=\{ a:a=(a_{1},\ldots, a_{n}), a_{1}>0,\ldots, a_{n}>0\}$.

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“…Yildirim, Sarikaya and Ozturk [3] showed that the function u(x) = (−1) k S 2k (x) * R 2k (x) is the unique elementary solution for the operator ♦ k B , where * indicates convolution, and R 2k (x), S 2k (x) are defined by (1.4) and (1.5) respectively, that is,…”

Section: Introductionmentioning

confidence: 99%

Solution of a partial differential equation related to the operator ⊕k b

Bupasiri¹

2017

Kragujevac J Math

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The solutions of then-dimensional Bessel diamond operator and the Fourier-Bessel transform of their convolution

Cited by 27 publications

References 4 publications

The compound equation related to the Bessel-Helmholtz equation and the Bessel-Klein-Gordon equation

The compound equation related to the Bessel-Helmholtz equation and the Bessel-Klein-Gordon equation

On the Bessel Operator $\odot_{B}^{t}$ Related to the Bessel-Helmholtz and Bessel Klein-Gordon Operator

Solution of a partial differential equation related to the operator ⊕k b

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