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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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An eigenfunction expansion for a nonselfadjoint, interior point boundary value problem
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by Allan M. Krall PDF
Trans. Amer. Math. Soc. 170 (1972), 137-147 Request permission

Abstract:

Under discussion is the vector system $Ly = y’ + Py,\sum \nolimits _{j = 0}^\infty {{A_j}y({t_j}) = 0}$, where $\sum \nolimits _{j = 0}^\infty {||A|| < \infty }$. The eigenvalues for the system are known to be countable and approach $\infty$ in the complex plane in a series of well-defined vertical steps. For each eigenvalue there exists an eigenmanifold, generated by the residue of the Green’s function. Further, since the Green’s function vanishes near $\infty$ in the complex plane when the path toward $\infty$ is horizontal, the Green’s function can be expressed as a series of its residues. This in turn leads to two eigenfunction expansions, one for elements in the domain of the original system, another for elements in the domain of the adjoint system.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 170 (1972), 137-147
  • MSC: Primary 34B25; Secondary 47E05
  • DOI: https://doi.org/10.1090/S0002-9947-1972-0311985-3
  • MathSciNet review: 0311985