The inverse spectral problem for canonical systems

Compressed Resolvents and Reduction of Spectral Problems on Star Graphs

“…7], [38,Thm. 1] to show that the linear relation T 1 in the reduced system in Theorem 4.1 can always be realized as a canonical system.…”

“…arising from L 2 H (e, C 2 ) by forming the factor space with respect to H -indivisable intervals (see [17,38]). InL 2 H (e, C 2 ) we consider the symmetric linear relation T defined as follows:…”

“…Note that also in the regular case < ∞ the right endpoint can be replaced by ∞, see [38], if H is extended to [ , ∞) by…”

“…[4,23]). Consider, for example, the Cauchy probleṁ [38,Thm. 1]) yields that every (scalar) Nevanlinna function is the Titchmarsh-Weyl function of a canonical system.…”

A unified approach to singular problems arising in the membrane theory

“…The function q H completely describes the spectrum of the problem (1.1) with boundary condition x 1 (0, z) = 0, and the measure in its Herglotz integral representation can be used to construct a generalized Fourier transform. The Inverse Spectral Theorem due to L. de Branges states that the assignment H → q H yields a bijection of the set of all Hamiltonians (up to changes of scale) and the set N 0 , see [5]- [8] and also [37]. The proof of this deep result is contained in de Branges' theory of Hilbert spaces of entire functions, cf.…”