Riesz Bases of Root Vectors of Indefinite Sturm-Liouville problems with eigenparameter dependent boundary conditions, I

We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions, one being affinely dependent on the eigenparameter. We give sufficient conditions under which a basis of each root subspace for this Sturm-Liouville problem can be selected so that the union of all these bases constitutes a Riesz basis of a corresponding weighted Hilbert space.Comment: 21 page

On infinite-dimensional differential equations

AbstractDifferential equations ·x(t) = f(x(t), t) are exhibited in a general infinite-dimensional Banach space, failing each of the following in turn. (i) The set St of solution values x(t) from a given point x(0) is compact. (ii) St is connected. (iii) Any point on the boundary ∂St of St can be reached by a solution x with x(s) ϵ ∂ Ss, 0 ⩽ s ⩽ t

An interview with Paul Binding

Paul Binding is a British writer who has worked in many fields: he is a literary critic, novelist, reviewer and renowned expert in Scandinavian literature. His novels are Harmonica’s Bridegroom (1984, recently reprinted by Valancourt Books), Kingfisher Weather (1989), My Cousin the Writer (2002) and After Brock (2013). He has given lectures at universities and participated in cultural events in Norway, Sweden, Denmark, Finland and Estonia. His memoir St Martin’s Ride, which focuses on his childhood in Germany soon after the end of the Second World War, was Sir Stephen Spender’s Book of the Year, and was awarded the J.R. Ackerley Prize for the best autobiographical book of 1990. He has frequently spent long periods abroad, and his time in Jackson, Mississipi as a visiting professor led to The Still Moment: Eudora Welty, Portrait of a Writer (1994). The book draws on the many conversations he had with Welty about her work. More recently, he published Imagined Corners: Exploring the World’s First Atlas (2003). He has frequently reviewed books for the Times Literary Supplement and The Independent. His most recent book is Hans Christian Andersen: European Witness (2014), which was very well reviewed and described by Amanda Craig in the Literary Review as his best work yet. An in-depth and wide-ranging literary biography, it sets Andersen’s work within a European context and pays close attention to his unjustly neglected work outside the fairy tales, such as the novel Improvisatore, which Binding argues was a great influence on Charles Dickens. I met and became friends with Paul through our mutual interest in the novelist Barbara Pym, and have since had many discussions with him about writers; he was the plenary speaker at the Barbara Pym Centenary Conference I organised in 2013. He lives in the beautiful small town of Bishop’s Castle, Shropshire, in the Welsh Marches – the border country of England and Wales. His website is http://www.paulbinding.co.uk/index.html

Riesz Bases of Root Vectors of Indefinite Sturm-Liouville Problems with Eigenparameter Dependent Boundary Conditions. II

We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions affinely dependent on the eigenparameter. We give sufficient conditions under which the root vectors of this Sturm-Liouville problem can be selected to form a Riesz basis of a corresponding weighted Hilbert space

The minimal index of a self-adjoint pencil

Let A and B be selfadjoint operators ona Hilbert space H. We define minimal index ν(A,B) = min {#negative eigenvalues of A - λB}, we connect it with various ideas in the literature and we connect it with formulae used in some recent variational principles

The minimal index of a self-adjoint pencil

Let A and B be selfadjoint operators ona Hilbert space H. We define minimal index ν(A,B) = min {#negative eigenvalues of A - λB}, we connect it with various ideas in the literature and we connect it with formulae used in some recent variational principles

Recovery of the m-function from spectral data for generalized Sturm–Liouville problems

AbstractThe Sturm–Liouville problem −y″+qy=λy, y(0)cosα=y′(0)sinα, (y′/y)(1)=h(λ)/g(λ) is studied, where h and g are real polynomials. Generalized norming constants ρnk associated with eigenvalues Λn are defined and formulae are given for recovering the m-function from these constants. This leads to a uniqueness theorem for the associated inverse problem

Form Domains and Eigenfunction Expansions for Differential Equations with Eigenparameter Dependent Boundary Conditions

Form domains are characterized for regular 2n-th order differential equations subject to general self-adjoint boundary conditions depending affinely on the eigenparameter. Corresponding modes of convergence for eigenfunction expansions are studied, including uniform convergence of the first n - 1 derivatives

A Counterexample in Sturm-Liouville Completeness Theory

We give an example of an indefinite weight Sturm-Lionville problem whose eigenfunctions form a Riesz basis under Dirichlet boundary conditions but not under anti-periodic boundary conditions