On Möbius’ inversion formula and closed sets of functions

On Möbius’ inversion formula and closed sets of functions
HTML articles powered by AMS MathViewer

by Otto Szász

Trans. Amer. Math. Soc. 62 (1947), 213-239

DOI: https://doi.org/10.1090/S0002-9947-1947-0021989-1

PDF | Request permission

References

Théorie des opérations linéaires

D. G. Bourgin, On certain sequences of functions, Proc. Nat. Acad. Sci. U.S.A. 32 (1946), 1–5. MR 14500, DOI 10.1073/pnas.32.1.1

On some infinite series involving arithmetical functions

Einar Hille, The inversion problem of Möbius, Duke Math. J. 3 (1937), no. 4, 549–568. MR 1546010, DOI 10.1215/S0012-7094-37-00344-2
Einar Hille and Otto Szász, On the completeness of Lambert functions, Bull. Amer. Math. Soc. 42 (1936), no. 6, 411–418. MR 1563312, DOI 10.1090/S0002-9904-1936-06319-6
Friedrich Riesz, Über eine Verallgemeinerung der Parsevalschen Formel, Math. Z. 18 (1923), no. 1, 117–124 (German). MR 1544624, DOI 10.1007/BF01192400
N. P. Romanov, On an orthogonal system, C. R. (Doklady) Acad. Sci. URSS (N.S.) 40 (1943), 257–258. MR 0010640
Otto Szász, Über die Approximation stetiger Funktionen durch lineare Aggregate von Potenzen, Math. Ann. 77 (1916), no. 4, 482–496 (German). MR 1511875, DOI 10.1007/BF01456964

Lectures on the analytic theory of numbers

Aurel Wintner, Diophantine approximations and Hilbert’s space, Amer. J. Math. 66 (1944), 564–578. MR 11497, DOI 10.2307/2371766

Trigonometrical series

D. G. Bourgin, A class of sequences of functions, Trans. Amer. Math. Soc. 60 (1946), 478–518. MR 20168, DOI 10.1090/S0002-9947-1946-0020168-0
Aurel Wintner, A solution theory of the Möbius inversion, Amer. J. Math. 68 (1946), 321–339. MR 16144, DOI 10.2307/2371845