×
Butzer, Paul L.; Sunouchi, G.

Approximation theorems for the solution of Fourier’s problem and Dirichlet’s problem. (English) Zbl 0178.12603

Math. Ann. 155, 316-330 (1964).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0178.12603

Cited in 6 Documents

Keywords:

partial differential equations
Cite Review PDF
Full Text: DOI EuDML

References:

[1] Aljan?i?, S.: Approximation of continuous functions by typical means of their Fourier series. Proc. Am. Math. Soc.12, 681-688 (1961). · Zbl 0101.28902
[2] Bochner, S.: Quasi-analytic functions, Laplace operator, positive kernels. Ann. Math.51, 68-91 (1950). · Zbl 0035.33102 · doi:10.2307/1969498
[3] Butzer, P. L.: Representation and approximation of functions by general singular integrals. Nederl. Akad. Wetensch. Proc. Ser. A.63 (= Indag. Math.22), 1-24 (1960). · Zbl 0107.32003
[4] Butzer, P. L., andH. G. Tillmann: Approximation theorems for semigroups of bounded linear transformations. Math. Ann.140, 256-262 (1960). · Zbl 0094.30602 · doi:10.1007/BF01361149
[5] Butzer, P. L.: Beziehungen zwischen den Riemannschen, Taylorschen und gewöhnlichen Ableitungen reellwertiger Funktionen. Math. Ann.144, 275-298 (1961). · Zbl 0106.27002 · doi:10.1007/BF01470502
[6] Carslaw, H. S.: Introduction to the theory of Fourier’s series and integrals and the mathematical theory of the conduction of heat. XVII + 434 pp. London 1906. · JFM 39.0975.01
[7] Doetsch, G.: Summatorische Eigenschaften der Besselschen Funktionen und andere Funktionalrelationen, die mit der linearen Transformationsformel der Thetafunktion äquivalent sind. Comp. Math.1, 85-89 (1934). · JFM 60.0306.01
[8] – Handbuch der Laplace-Transformation, Band I. 581 pp. Basel 1950.
[9] Hille, E.: Functional Analysis and Semi-Groups. 528 pp. New York 1948. · Zbl 0033.06501
[10] Leis, R.: Approximationssätze für stetige Operatoren. Arch. Math.14, 120-129 (1963). · Zbl 0196.43303 · doi:10.1007/BF01234932
[11] Minakshisundaram, S.: Studies in Fourier Ansatz and parabolic equations. I. J. Madras Univ.14, 73-142 (1942). · Zbl 0061.22102
[12] Sunouchi, G., andC. Watari: On determination of the class of saturation in the theory of approximation of functions. I. Proc. Japan Acad.34, 477-481 (1959); II. Tôhoku Math. J.11, 480-488 (1959). · Zbl 0086.05502 · doi:10.3792/pja/1195524556
[13] Sunouchi, G.: On the saturation and best approximation. Tôhoku Math. J.14, 212-216 (1962). · Zbl 0109.29203 · doi:10.2748/tmj/1178244176
[14] ?? On the Riesz summability of Fourier Series. Tôhoku Math. J.11, 321-326 (1959). · Zbl 0091.24901 · doi:10.2748/tmj/1178244591
[15] Zygmund, A.: Trigonometrical Series. Vol. I. IX + 383 pp. (revised edition). Cambridge 1959. · Zbl 0085.05601
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.