The Variational Approach to Linear Boundary and Eigenvalue Problems

1992 ◽  
pp. 142-170
Author(s):  
Philippe Blanchard ◽  
Erwin Brüning
Keyword(s):  
Variational Approach ◽  
Eigenvalue Problems ◽  
Linear Boundary

Self-adjoint subspace extensions satisfying λ-linear boundary conditions

1981 ◽  
Vol 90 (1-2) ◽  
pp. 107-124 ◽  
Author(s):  
Harald Röh
Keyword(s):  
Hilbert Space ◽  
Boundary Conditions ◽  
Hilbert Spaces ◽  
Eigenvalue Problems ◽  
Linear Boundary ◽  
Deficiency Indices ◽  
Symmetric Subspace

SynopsisLet S be a symmetric subspace in a Hilbert space ℋ2 with finite equal deficiency indices and let S* be its adjoint subspace in ℋ2. We consider those self-adjoint subspace extensions ℋ of S into some larger Hilbert spaces ℋ2 = (ℋ × ℂm)2 which satisfy H⋂({0} × ℂm)2 = {{0,0}}. These extensions H are characterized in terms of inhomogeneous boundary conditions for S*; they are associated with eigenvalue problems for S* depending on λ-linear boundary conditions, which we also characterize.

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