Titlebook: Algebraic Analysis of Differential Equations; from Microlocal Anal Takashi Aoki,Hideyuki Majima,Nobuyuki Tose Book 2008 Springer-Verlag Tok

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Ghost busting: Making sense of non-Hermitian Hamiltoniansy. The proof of unitarity requires the construction of a time-independent operator called .. In terms of . one can define a new inner product with respect to which the norms of the states in the Hilbert space are positive. Furthermore, it has been shown that time evolution in such a theory is unitar

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https://doi.org/10.1007/978-4-431-73240-2Boundary value problem; Complex analysis; Microlocal analysis; Painlev/‘e equations; algebraic analysis;

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Automated Debugging for Logic Bugsts importance in the analysis of the Noumi-Yamada system (a particular higher order Painlevé equation) and a concrete recipe for locating them. Examples given here make it manifest that virtual turning points are indispensable in WKB analysis of higher order linear ordinary differential equations wi

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https://doi.org/10.1007/978-3-319-06242-6 0 (say, . = (?1).). If . = 1 we assume .(0, ·) is meromorphic and nonlinear. If . = 2, we assume .(0, ·) is analytic except for isolated singularities, and also that ∫. |.(.)|..|.| < ∞ along some path avoiding the zeros and singularities of ., where .(.) = ∫..(0, .).. Let .. = {z: |.| > . > 0, arg(