Adjoint subspaces in Banach spaces, with applications to ordinary differential subspaces

DOI10.1007/BF02415124zbMath0408.47035MaRDI QIDQ1258511

Aalt Dijksma, Earl A. Coddington

Publication date: 1978

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

zbMATH Keywords

Adjoint SubspacesGeneralized Boundary ConditionsOrdinary Differential Subspaces

Mathematics Subject Classification ID

Normed linear spaces and Banach spaces; Banach lattices (46B99) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) General theory of ordinary differential operators (47E05) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05) Linear boundary value problems for ordinary differential equations (34B05)

Related Items (30)

Gradient Method for Nondensely Defined Closed Unbounded Linear Operators ⋮ Local Completeness for Eigenfunctions of Regular Maximal Ordinary Differential Operators ⋮ The adjoint problem for coupled linear operators ⋮ Constrained least-squares solutions of linear inclusions and singular control problems in Hilbert spaces ⋮ Boundary conditions for quasi-differential operators in \(L^p\) spaces ⋮ Boundary conditions for linear manifolds. I ⋮ Solutions of bounded variation of linear integro-differential equations ⋮ \(\mathcal C\)-symmetric Hamiltonian systems with almost constant coefficients ⋮ Genericity of simple eigenvalues ⋮ Boundary conditions for linear manifolds. II: Algebraic properties and applications ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Operator part of infinite system of differential equations ⋮ Boundary conditions for linear manifolds. III: Infinite dimensional adjoints via solution spaces ⋮ Normed linear relations: Domain decomposability, adjoint subspaces, and selections ⋮ Finite-dimensional Self-adjoint Extensions of a Symmetric Operator with Finite Defect and their Compressions ⋮ Generalized boundary value problems with abstract side conditions and their adjoints. II ⋮ Boundedness and closedness of linear relations ⋮ Iteration scheme for nondensely defined ordinary differential operator equation ⋮ Pointwise convergence of eigenfunction expansions, associated with a pair of ordinary differential expressions ⋮ Operators generated by countably many differential operators ⋮ Eigenfunction expansions for a class of J-selfadjoint ordinary differential operators with boundary conditions containing the eigenvalue parameter ⋮ Differential subspaces associated with pairs of ordinary differential expressions ⋮ Unnamed Item ⋮ Self-adjoint subspace extensions satisfying λ-linear boundary conditions ⋮ Nonhomogeneous boundary value problems for linear manifolds ⋮ Least-squares solutions of multi-valued linear operator equations in Hilbert spaces ⋮ Dense linear manifolds and application to linear differential operators ⋮ Eigenfunction expansions associated with pairs of ordinary differential expressions ⋮ Infinitely many nonhomogeneous conditions

Cites Work

• Functional analysis and partial differential equations. I
• Selfadjoint subspaces and eigenfunction expansions for ordinary differential subspaces
• The development of general differential and general differential-boundary systems
• On the complemented subspaces problem
• Extension theory of differential operators I
• Extension theory of formally normal and symmetric subspaces
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