On some perturbations of a stable process and solutions to the Cauchy problem for a class of pseudo-differential equations
2015 ◽
Vol 7
(1)
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pp. 101-107
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Keyword(s):
A fundamental solution for some class of pseudo-differential equations is constructed by the method based on the theory of perturbations. We consider a symmetric $\alpha$-stable process in multidimensional Euclidean space. Its generator $\mathbf{A}$ is a pseudo-differential operator whose symbol is given by $-c|\lambda|^\alpha$, were the constants $\alpha\in(1,2)$ and $c>0$ are fixed. The vector-valued operator $\mathbf{B}$ has the symbol $2ic|\lambda|^{\alpha-2}\lambda$. We construct a fundamental solution of the equation $u_t=(\mathbf{A}+(a(\cdot),\mathbf{B}))u$ with a continuous bounded vector-valued function $a$.
2018 ◽
Vol 20
(03)
◽
pp. 1750046
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Keyword(s):
2005 ◽
Vol 42
(2)
◽
pp. 115-130
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1996 ◽
Vol 06
(03)
◽
pp. 295-314
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1956 ◽
Vol 8
◽
pp. 426-431
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2003 ◽
Vol 8
(1)
◽
pp. 61-75
2017 ◽
Vol 41
(3)
◽
pp. 113-121