Abstract
In the present chapter we pay special attention to zeros of L(t, D t ) both on ℝ, and the semiaxis t > t 0. We restrict ourselves to the zeros subject to a certain growth restriction which is formulated in terms of Green’s functions of two auxiliary ordinary differential equations (see Sect. 8.3). We show, in particular, that the space X(L) of the zeros on ℝ is finite dimensional, find its dimension and obtain upper and lower estimates for its elements. Similar results are obtained for zeros of the adjoint operator on ℝ in Sect. 8.4. The biorthogonality condition (2.13) is extended to zeros of L and L* in Sect. 8.4.4.
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© 1999 Springer-Verlag Berlin Heidelberg
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Kozlov, V., Maz’ya, V. (1999). Connection of Solutions Corresponding to Different Strips. In: Differential Equations with Operator Coefficients. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-11555-8_8
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DOI: https://doi.org/10.1007/978-3-662-11555-8_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08453-9
Online ISBN: 978-3-662-11555-8
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