A Course In Functional Analysis

By K. Rothschild. 2016

1,899 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/a0618ab3a692102d16ecaad7be96e4eef66c226f

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Citations in the corpus

Dynamical sampling (2014, unknown): “The methods that we develop for studying the dynamical sampling problem are related to methods in spectral theory, operator algebras, and frame theory [2, 10, 13, 15, 18, 20, 21, 22, 45].”
Functional Data Analysis (2016, methodology): “…smoothing methods, notably kernel, local least squares and spline smoothing for which various excellent reference books exist (Wand & Jones 1995; Fan & Gijbels 1996; Eubank 1999; de Boor 2001), functional analysis (Conway 1994; Hsing & Eubank 2015) and stochastic processes (Ash & Gardner 1975).”
Sobolev Spaces on Non-Lipschitz Subsets of Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^n$$\end{doc (2016, unknown): “We recall that an isomorphism between Hilbert spaces is unitary if and only if it is isometric [16, Proposition 5.2].”
The predual and John-Nirenberg inequalities on generalized BMO martingale spaces (2014, background): “ties of martingale Hardy-Lorentz spaces for 0 <p≤ 1,1 <q<∞. It is well known that the dual spaces of Lebesgue spaces Lp or Lorentz spaces Lp,q are trivial when 0 <p<1 (see for instance [5] or [9]), namely, Lp ∗ = Lp,q ∗ = {0}, (0 <p<1,0 <q≤ ∞). However, the dual spaces of mar”
Isometries of the unitary groups and Thompson isometries of the spaces of invertible positive elements in C*-algebras (2014, methodology): “Applying Stone’s theorem (see Section 5 in Chapter X in [2]) for the norm continuous one-parameter unitary group (Sx(t))t∈R, we infer that there exists a unique bounded self-adjoint operator y on H2 such that Sx(t) = exp(ity) holds for every t ∈ R (the boundedness of y is the consequence of the norm”
Envelopes and reduced-rank regression (2015, methodology): “…to be a reducing subspace of M ∈ Rr×r, or equiva-131 lently sayingR reduces M, if and only ifR decomposes M as M = PRMPR + QRMQR.132 The definition of a reducing subspace is basic in functional analysis (Conway 1990) but the133 notion of reduction is different from the common statistical meaning.”
Iterative actions of normal operators (2016, methodology): “A proof of the theorem can be found in [12] (Ch.”