ISSN:
1618-1891
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary Given two subspaces A0 ⊂ A1 ⊂ W=X ⊕ Y, where X, Y are Banach spaces, we show how to characterize, in terms of generalized boundary conditions, those adjoint pairs A, A* satisfying A0 ⊂ A ⊂ A1, A 1 * ⊂ A∗ ⊂ A 0 * ⊂ W+=Y* ⊕ X*, where X*, Y* are the conjugate spaces of X, Y, respectively. The characterizations of selfadjoint (normal) subspace extensions of symmetric (formally normal) subspaces appear as special cases when Y=X*. These results are then applied to ordinary differential subspaces in W=Lq(ι) ⊕ Lr(ι), 1≦q, r≦∞, where τ is a real interval, and in W=C( $$\bar \iota $$ ) ⊕ C( $$\bar \iota $$ ), where $$\bar \iota $$ is a compact interval.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02415124
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