Rocky Mountain Journal of Mathematics

Spectral representation of self adjoint extensions of a symmetric operator

Richard C. Gilbert

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Article information

Rocky Mountain J. Math., Volume 2, Number 1 (1972), 75-96.

First available in Project Euclid: 13 August 2009

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 47A20: Dilations, extensions, compressions 47B25: Symmetric and selfadjoint operators (unbounded) 47A10: Spectrum, resolvent
Secondary: 47E05: Ordinary differential operators [See also 34Bxx, 34Lxx] (should also be assigned at least one other classification number in section 47)

Symmetric operator deficiency indices selfadjoint operator selfadjoint extension spectrum spectral multiplicity spectral function generalized spectral function spectral matrix spectral representation multiplication operator singular Sturm-Liouville operator Cayley transform isometric operator unitary operator unitary extension generating subspace analytic function with nonnegative imaginary part resolution of the identity resolvent generalized resolvent generalized resolution of the identity.


Gilbert, Richard C. Spectral representation of self adjoint extensions of a symmetric operator. Rocky Mountain J. Math. 2 (1972), no. 1, 75--96. doi:10.1216/RMJ-1972-2-1-75.

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