Abstract
So far we have spent a great deal of time focusing our attention on bounded operators, when, indeed, our interest is in dealing with differential operators which are unbounded. The reason for this is that in order to properly attack the problems associated with them, a foundation concerning bounded operators must be laid first. The spectral resolution for a bounded self-adjoint operator,
but the proof, which is considerably more complicated, is derived by looking at a certain unitary operator, the Cayley transform. Hence the need for the preceding work. We follow the path ingeniously described by John von Neumann.
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References
N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hilbert space, vol. I and II, Frederick Ungar, New York, 1961.
A. M. Krall, Applied Analysis, D. Reidel, Dordrecht, 1986.
F. Riesz and B. Sz.-Nagy, Functional Analysis, Frederick Ungar, New York, 1955.
A.E. Taylor, Introduction to Functional Analysis, John Wiley and Sons, New York, 1958.
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© 2002 Springer Basel AG
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Krall, A.M. (2002). Unbounded Linear Operators On a Hilbert Space. In: Hilbert Space, Boundary Value Problems and Orthogonal Polynomials. Operator Theory: Advances and Applications, vol 133. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8155-5_3
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DOI: https://doi.org/10.1007/978-3-0348-8155-5_3
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9459-3
Online ISBN: 978-3-0348-8155-5
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