![]() ![]() This setup has important applications, but only a few theoretical studies are available. ![]() Continued fraction Jacobi matrix Moment problem). The authors study ill-posed equations with unbounded operators in Hilbert space. Stieltjes on the classical problems of moments, Jacobi matrices and continued fractions (cf. Note that both for the investigations by Hilbert, and for much later investigations, the works of P.L. For this to be true, we need the space to be a reproducing kernel Hilbert space which we. Note that jjf n fjj0 does NOT imply that f n(x) f(x). In a Hilbert space, we write f nf to mean that jjf n fjj0 as n1. Every Hilbert space is a Banach space but the reverse is not true in general. The importance of the concept of a self-adjoint operator was first drawn attention to by Schmidt (cf. A Hilbert space is a complete, inner product space. Carleman, who obtained the spectral decomposition for the case of a symmetric integral operator, and who also discovered that there is no complete analogy between symmetric bounded and unbounded operators. His work preceded the important investigations of T. The spectral decomposition of an unbounded self-adjoint operator was found by von Neumann. One of the most profound is given by the theory of Banach algebras. Nowadays, several approaches to the spectral theory of self-adjoint and normal operators are available. A Hilbert space 2 (H h i)3 is a complete inner product space. The spectral decomposition was found by Hilbert, who also introduced the important concept of a resolution of the identity for a self-adjoint operator. Over the field of complex (or real) numbers, together with a complex-valued (or real-valued) function $ ( x, y) $ĥ) $ ( x, y) = \overline $ ![]()
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