Motivated by the idea of J-frame for a Krein space K , introduced by Giribet et al. (J. I. Giribet, A. Maestripieri, F. Martnez Peŕıa, P. G. Massey, On frames for Krein spaces, J. Math. Anal. Appl. (1), 393 (2012), 122–137.), we introduce the notion of ζ − J-tight frame for a Krein space K . In this paper we characterize J-orthonormal basis for K in terms of ζ−J-Parseval frame. We show that a K...

We show that the classical Hamburger moment problem can be included in the spectral theory of generalized indefinite strings. Namely, we introduce the class of Krein–Langer strings and show that there is a bijective correspondence between moment sequences and this class of generalized indefinite strings. This result can be viewed as a complement to the classical results of M. G. Krein on the co...

It is shown that there is no Hausdorff vector topology p on the space Lp (where 0 < p < 1) such that the unit ball of Lp is relatively compact for the topology p. It is well known that the space L1 (0, 1) is not a dual Banach space; this follows from the Krein-Milman theorem. It is not even isomorphic to a dual space, by a result due to Gelfand [2] (see Bessaga and Pelczyn'ski [1] and Namioka [...

Krein space operator-theoretic methods are used to prove that the operator (sgn x) d is similar to a selfadjoint operator in the Hilbert space L2 (R) . Let L be a symmetric ordinary differential expression. Spectral properties of the operators associated with the weighted eigenvalue problem Lu = )wu have been studied extensively. When w is positive, this problem leads to a selfadjoint problem i...

It is shown that every regular Krein-Feller eigenvalue problem can be transformed to a semidefinite Sturm-Liouville problem introduced by Atkinson. This makes it possible to transfer results between the corresponding theories. In particular, Prüfer angle methods become available for Krein-Feller problems.

Krein space operator-theoretic methods are used to prove that the operator (sgnx)-j-j is similar to a selfadjoint operator in the Hubert space ¿2(R) • Let L be a symmetric ordinary differential expression. Spectral properties of the operators associated with the weighted eigenvalue problem Lu = Xwu have been studied extensively. When w is positive, this problem leads to a selfadjoint problem in...

We consider the Krein realization of the Hilbert space for a massless scalar field in 1+1 dimensions. We find convergence criteria and the completion of the space of test functions S with the topology induced by the Krein scalar product. Finally, we show that the interpretation for the Fourier components as probability amplitudes for the momentum operator is lost in this case.

Whitney's extension problem asks the following: Given a compact set E?Rn and function f:E?R, how can we tell whether there exists F?Cm(Rn) such that F=f on E? A 2006 theorem of Charles Fefferman [6] answers this question in its full generality. In paper, establish version adapted for variants Whitney problem, including nonnegative extensions smooth selection problems. Among other things, genera...