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Browsing by Subject "initial function"

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    Item type:Article, Access status: Open Access ,
    Eigenvalue-eigenfunction problem for Steklov's smoothing operator and differential-difference equations of mixed type
    (2013) Âkovlev, Sergej I.; Âkovleva, Valentina
    It is shown that any $\mu \in \mathbb{C}$ is an infinite multiplicity eigenvalue of the Steklov smoothing operator $S_h$ acting on the space $L^1_{loc}(\mathbb{R})$. For $\mu \neq 0$ the eigenvalue-eigenfunction problem leads to studying a differential-difference equation of mixed type. An existence and uniqueness theorem is proved for this equation. Further a transformation group is defined on a countably normed space of initial functions and the spectrum of the generator of this group is studied. Some possible generalizations are pointed out.