author={Errett Bishop},
  journal={Transactions of the American Mathematical Society},
  • E. Bishop
  • Published 1 March 1962
  • Mathematics
  • Transactions of the American Mathematical Society
Fractional calculi on parabolic Hardy spaces
For a triple of n × n Hermitian matrices (H1,H2,H3) and a real sequence c ∈ R, the c-joint c-numerical range Wc(H1,H2,H3) is realized as the joint numerical range W (K1,K2,K3) of some triple of N × N
Introduction. By a function algebra I shall mean a collection A of complex-valued functions on a set X such that the (pointwise) sum and the product of two functions in A are again in A. We shall
Envelopes of holomorphy of Jordan curves in ℂn
A comprehensive answer is given to two related questions: (i) Can continuous functions be approximated by holomorphic ones on Jordan curves in ℂn (A.G. Vitushkin, 1964)? (ii) Is any Jordan curve in
Polynomial hulls and positive currents
Nous decrivons a la suite des travaux de Wermer, l'enveloppe polynomiale des ensembles compacts contenus dans le bord d'un domaine lisse strictement convexe de C n . Nous etendons aussi ce resultat
On positive plurisubharmonic currents
Let T be a positive plurisubharmonic current of bidimension (p,p) and \delta>0. Assume that the Lelong number of T satisfies \nu(T,a)\geq \delta on a dense subset of \supp(T) (rectifiable currents
Enveloppe polynomiale d'un compact de longueur finie et chaînes holomorphes à bord rectifiable
0. Introduction 1. D~finitions et lemmes pr~paratoires 2. Enveloppe polynomiale d'un compact de longueur finie 3. Chalnes holomorphes ~ bord rectifiable dans C" 4. D~monstration du th~or~me 3.1 pour
Orthogonal Measures on the Boundary of a Riemann Surface and Polynomial Hull of Compacts of Finite Length
Letμbe an orthogonal measure with compact support of finite length in Cn. We prove, under a very weak hypothesis of regularity on the support (Supp μ) ofμ, that this measure is characterized by its
Surfaces de Riemann de bord donne dans CPn
Soit X une variete analytique complexe, de dimension complexe n. Soit γ une courbe reelle fermee orientee, ou plus generalement une 1-chaine fermee de classe C k , alors bγ = O. S’il existe une
On analytic disks in the spectrum of a uniform algebra


Dimension theory, Princeton Univ
  • Press, Princeton, N. J.,
  • 1948
Eine elementarer Beweis des Satzes von Radó-Behnke-Stein-Cartan über analytischen Funktionen
  • Math. Ann
  • 1956
Subalgebras of functions on a Riemann surface.
An example concerning polynomial convexity
Let K be a compact set in the space C n of n complex variables. The polynomiaUy convex hull of K, written h(K), is defined to be the set of points x in C n which satisfy IP(x)l < max [P(y)I for all
Abstract Harmonic Analysis
The first € price and the £ and $ price are net prices, subject to local VAT. Prices indicated with * include VAT for books; the €(D) includes 7% for Germany, the €(A) includes 10% for Austria.
Theory of Lie Groups
This famous book was the first treatise on Lie groups in which a modern point of view was adopted systematically, namely, that a continuous group can be regarded as a global object. To develop this
Theory of Lie groups, Princeton Univ
  • Press, Princeton, N. J.,
  • 1949
It follows that S' can uniquely be given the structure of a Riemann surface in such a way that the maps ai are all analytic. As a consequence the functions /' in 21' are all analytic on S
  • ¿£P} for all/ in 21. Since the Ui cover S there exists « with KCUn. Since g(7") giln+i)f~^giyn+i) is void we may choose m with #(g)£g(7m), where m = n, »+1, or ra+2. Thus K(ZUm. Therefore U(/)| ásup{ \f