Celebratio Mathematica — Whitney

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Works connected to Harold Calvin Marston Morse

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A. M. Gleason and H. Whitney: “The extension of linear functionals defined on \( H^{\infty} \),” Pacific J. Math. 12 : 1 (1962), pp. 163–182. Dedicated to Marston Morse. MR 0142013 Zbl 0191.15202 article

We consider the Banach space \( L^{\infty} \) of (classes of) bounded measurable complex functions on the unit circle \( \Gamma_1 \). It has a subspace \( H = H^{\infty} \) consisting of those functions \( h \) which are the boundary value functions (existing almost everywhere by Fatou’s theorem) of bounded analytic functions \( \hat{h} \) in the interior \( S_1 \) of \( \Gamma_1 \). By the Hahn–Banach theorem, any bounded linear functional \( \varphi \) defined on \( H^{\infty} \) can be extended over \( L^{\infty} \) with no increase in norm. It is the primary purpose of this paper to prove that this extension is unique, provided that \( \varphi \) is defined (over \( H \)) by an integral with kernel in \( L^1 \). Without this hypothesis, uniqueness may fail.

Andrew Mattei Gleason	Related	Volume
Harold Calvin Marston Morse	Related

H. Whitney: “Local properties of analytic varieties,” pp. 205–244 in Differential and combinatorial topology: A symposium in honor of Marston Morse (Institute for Advanced Study, Princeton, NJ, 1964). Edited by S. S. Cairns. Princeton Mathematical Series 27. Princeton University Press, 1965. MR 0188486 Zbl 0129.39402 incollection

Harold Calvin Marston Morse	Related
Stewart Scott Cairns	Related