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(23 citation statements)

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“…Indeed, Equation can be written as $${\left(p{u}^{\prime}\right)}^{\prime}+\left(q-{\lambda}^{*}r\right)u=\left(\lambda -{\lambda}^{*}\right)\mathrm{ru},$$ then the same arguments that were used to prove Proposition 5 and Theorem 7 can be applied. The procedure for constructing solutions of Equation based on a particular solution f * corresponding to λ = λ * is known as the spectral shift and is of great practical importance especially in numerical applications .…”

confidence: 99%

“…Indeed, Equation can be written as $${\left(p{u}^{\prime}\right)}^{\prime}+\left(q-{\lambda}^{*}r\right)u=\left(\lambda -{\lambda}^{*}\right)\mathrm{ru},$$ then the same arguments that were used to prove Proposition 5 and Theorem 7 can be applied. The procedure for constructing solutions of Equation based on a particular solution f * corresponding to λ = λ * is known as the spectral shift and is of great practical importance especially in numerical applications .…”

confidence: 99%

“…13) we obtainR(x) = x Re 2R 1 (c 1 ) + c1 0 q(s)R(s)ds + ix Im 2R 1 (c 2 ) +c2 0 q(s)R(s)ds = x Re (o(x n ) + o(x n+1 )) + i Im (o(x n ) + o(x n+1 )) = o(x n+1 ). …”

mentioning

confidence: 98%

“…In [33] it was mentioned that for equation (1.2) it is also possible to construct the SPPS representation of a general solution starting from a non-vanishing particular solution for some λ = λ 0 . Such procedure is called spectral shift and has already proven its usefulness for numerical applications [9,21,33].…”

confidence: 99%

“…As was shown in a number of recent publications the SPPS representation provides an efficient and accurate method for solving initial value, boundary value and spectral problems (see [7], [8], [16], [21], [23], [22], [24], [25], [31], [32], [33], [35], [47]). In this paper we demonstrate this fact in application to equation (1.1).…”

confidence: 99%