Theory of linear operators in Hilbert space

By N. Akhiezer, I. M. Glazman. 1961

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “The next theorem known as Riesz representation theorem provides a characterization of a bounded linear operator in H (see, e.g., Akhiezer and Glazman (1993) for the proof).”
Spectral Properties of Dynamical Systems, Model Reduction and Decompositions (2005, background): “It should be clear that the zero-mean field vap(n, x,m) is almost periodic in the sense of Bohr in the variable n [2].”
The Analytic Theory of Matrix Orthogonal Polynomials (2007, background): “Consider Ml ⊕Ml = Ml[2] as a right module over Ml.”
Linear Stochastic Systems: A Geometric Approach to Modeling, Estimation and Identification (2016, unknown): “y(t) = [ 1 1 2 ] x(t)”
On Learning Vector − Valued Functions (2003, methodology): “In this case, according to the Riesz Lemma (see, e.g., [1]), there is, for every x ∈ X and y ∈ Y a function K ( x | y ) ∈ H such that, for all f ∈ H , ( y, f ( x )) = h K ( x | y ) , f i .”
Stability of impulsive time-varying systems and compactness of the operators mapping the input space into the state and output spaces (2006, methodology): “The last part of the manuscript is devoted to investigate the compactness of the various operators (see, for instance, [14,15] for definitions and relevant properties) mapping the input into state and output Banach’s spaces if the input is square-integrable on [0,∞).”
Robin-to-Robin Maps and Krein-Type Resolvent Formulas for Schr\ (2008, methodology): “An attractive feature of the Krein-type formula (4.41) lies in the fact that M (0) Θ,D,Ω(z) encodes spectral information about ∆Θ,Ω.”
Quantum graphs: I. Some basic structures (2004, methodology): “This is done by either using the standard von Neumann theory of extensions of symmetric operators (as for instance described in [ 1 ]), or by its more recent version that amounts to finding Lagrangian planes with respect to the complex symplectic boundary form that corresponds to the maximal operato”
Continuous analogs of polynomials orthogonal on the unit circle. Krein systems (2009, background): “0 [g(x− y) − g(x) − g(−y)] exp(ixz − iyz)dxdy ≤ 0 Consequently, −iL(z) is Herglotz function and has well-known integral representation ([4], chapter 6) which gives”
On the Point-Particle (Newtonian) Limit¶of the Non-Linear Hartree Equation (2002, background): “in the sense that is small as compared to the kinetic energy operator of two bosons, in the sense of Kato and Rellich, [2]).”