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Schauder-type expansions of continuous functions on the unit interval. (English) Zbl 0341.41027

MSC:

41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
41A45 Approximation by arbitrary linear expressions
42C15 General harmonic expansions, frames
42A65 Completeness of sets of functions in one variable harmonic analysis
46A35 Summability and bases in topological vector spaces
40A05 Convergence and divergence of series and sequences
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References:

[1] Ciesielski, Z., Lectures on Brownian motion, heat conduction and potential theory (1966), Mathematics Institute, Aarhus University · Zbl 0232.60060
[2] Finlayson, H. C., Approximation of Wiener integrals of functionals continuous in the uniform topology, Pacific J. Math., 34, 61-71 (1970) · Zbl 0199.20601
[3] Finlayson, H. C., The expansion of continuous functions in series of integrals of orthonormal functions, Glasgow Math. J., 13, 29-37 (1972), (part 1) · Zbl 0258.42022
[4] Gross, L., Measurable functions on Hilbert space, Trans. Amer. Math. Soc., 105, 372-390 (1962) · Zbl 0178.50001
[5] Gross, L., Potential theory on Hilbert space, J. Functional Analysis, 1, 123-181 (1967) · Zbl 0165.16403
[6] Hida, T., Stationary Stochastic Processes, (Mathematical Notes (1970), Princeton Univ. Press: Princeton Univ. Press Princeton, N. J) · Zbl 0214.16401
[7] E. W. Hobson; E. W. Hobson · JFM 38.0414.01
[8] Wiener, N., Generalized harmonic analysis, Acta Math., 55, 117-258 (1930) · JFM 56.0954.02
[9] Yeh, J., Stochastic Processes and the Wiener Integral (1973), Dekker: Dekker New York · Zbl 0277.60018
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