Hilbert spaces generated by positive selfadjoint extensions of Mo

1981 ◽  
pp. 54-63
Author(s):  
Earl A. Coddington ◽  
Hendrik S. V. de Snoo
Keyword(s):  
Hilbert Spaces ◽  
Selfadjoint Extensions

scholarly journals Normal extensions of a first order differential operator

Filomat ◽  
2014 ◽  
Vol 28 (5) ◽  
pp. 917-923
Author(s):  
Z.I. Ismailov ◽  
M. Sertbaş ◽  
B.Ö. Güler
Keyword(s):  
Differential Expression ◽  
Hilbert Spaces ◽  
Nonlocal Boundary ◽  
Order Differential Operator ◽  
Scalar Case ◽  
Minimal Operator ◽  
First Order ◽  
Direct Sum ◽  
Fixed Order ◽  
Selfadjoint Extensions

In the paper of W.N. Everitt and A. Zettl [26] in scalar case, all selfadjoint extensions of the minimal operator generated by Lagrange-symmetric any order quasi-differential expression with equal deficiency indexes in terms of boundary conditions are described by Glazman-Krein-Naimark method for regular and singular cases in the direct sum of corresponding Hilbert spaces of functions. In this work, by using the method of Calkin-Gorbachuk theory all normal extensions of the minimal operator generated by fixed order linear singular multipoint differential expression l = (l-, l1,... ln, l+), l-+ = d/dt + A-+, lk = d/dt + Ak where the coefficients A-+, Ak are selfadjoint operator in separable Hilbert spaces H-+, Hk, k= 1,..., n, n ? N respectively, are researched in the direct sum of Hilbert spaces of vector-functions L2(H_, (-? a))? L2(H1, (a1, b1)) ?...? L2(Hn, (an, bn)) ? L2(H+, (b,+?)) -? < a < a1 < b1 < . .. < an < bn < b < +?. Moreover, the structure of the spectrum of normal extensions is investigated. Note that in the works of A. Ashyralyev and O. Gercek [2, 3] the mixed order multipoint nonlocal boundary value problem for parabolic-elliptic equation is studied in weighed H?lder space in regular case.

Unbounded Linear Operators

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Von Neumann ◽  
Limit Circle ◽  
Sectorial Operators ◽  
Closed Operators ◽  
The Stability ◽  
Symmetric Operators ◽  
Unbounded Linear Operators ◽  
Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

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