Square Summable Power Series

By L. Branges, J. Rovnyak. 2014

173 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/4adfeef6b85372e9fd0e0a4e8bcf56f3b265be30

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Boundary Value Problems, Weyl Functions, and Differential Operators (2020, background): “We remind the reader that special reproducing kernels were considered by de Branges and Rovnyak for the setting of Nevanlinna functions or Schur functions [146, 147, 148, 149, 150, 151, 152, 153]; see also [24, 25, 33].”
Noncommutative reproducing kernel Hilbert spaces (2016, background): “nel KS(z,w) = IY−S(z)S(w)∗ 1−zw has become known as a de Branges-Rovnyak kernel and the associated Hilbert space H(KS) as a de Branges-Rovnyak space, due to the fundamental work of de Branges-Rovnyak [20, 21] (see also [7, 12, 37, 38, 39, 44]). Much of the theory associated with these spaces goes th”
Spectral radius of semi-Hilbertian space operators and its applications (2019, background): “Rovnyak in [9] shows that the completion of H∕N(A) under the inner product [⋅, ⋅] is isometrically isomorphic to the Hilbert space R(A) with the inner product”
A-Numerical Radius Orthogonality and Parallelism of Semi-Hilbertian Space Operators and Their Applications (2020, background): “However, a canonical construction due to L. de Branges and J. Rovnyak in [12] shows that the completion of H / N ( A ) under the inner product [ · , · ] is isometrically isomorphic to the Hilbert space R ( A 1 / 2 ) with the inner product ( A 1 / 2 x, A 1 / 2 y ) = h P A x | P A y i , ∀ x, y ∈ H .”
Ergodic properties of operators in some semi-Hilbertian spaces (2013, background): “A canonical construction due to de Branges and Rovnyak 4 shows that the completion of ℋ / 𝒩( A ) is isometrically isomorphic to the Hilbert space ℛ( A 1/2 ) with the inner product where P denotes the orthogonal projection of ℋ onto the closure of ℛ( A ).”
Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis (2013, background): “ernel k s(;). This space provides a coisometric realization of scalled the backward shift realization of s, which is already present (maybe in an implicit way) in the work of de Branges and Rovnyak [21]. See for instance Problem 47, p. 29 in that book. Theorem 6.1.2. The operators A[f](z) := f(z) f(”