Polynomials and the limit point condition

Author:
Robert M. Kauffman

Journal:
Trans. Amer. Math. Soc. **201** (1975), 347-366

MSC:
Primary 47E05; Secondary 34B20

DOI:
https://doi.org/10.1090/S0002-9947-1975-0358438-7

MathSciNet review:
0358438

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Abstract: An th order, possibly nonselfadjoint, ordinary differential expression is said to be in the limit point condition if the maximal operator in is an -dimensional extension of the minimal operator . If range is closed, this definition is equivalent to the assertion that nullity nullity, where is the formal adjoint of . It also implies that any operator such that is the restriction of to a set of functions described by a boundary condition at zero. In this paper, we discuss the question of when differential expressions involving complex polynomials in selfadjoint expressions are in the limit point condition.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1975-0358438-7

Keywords:
Limit point condition,
minimal operator,
maximal operator,
Fredholm operator,
perturbation theory,
product of operators,
complex polynomials in a formally selfadjoint expression

Article copyright:
© Copyright 1975
American Mathematical Society