• [1] Torsten Carleman, Über die Fourierkoeffizienten einer stetigen Funktion, Acta Math. 41 (1916), no. 1, 377–384 (German). Aus einem Brief an Herrn A. Wiman. MR 1555157, http://dx.doi.org/10.1007/BF02422951
• [1] M. L. Cartwright On analytic functions regular in the unit circle, Quart. J. Math. Oxford Ser. vol. 4 (1933) pp. 246-257.
• [1] J. H. Curtiss, A note on the degree of polynomial approximation, Bull. Amer. Math. Soc. 42 (1936), no. 12, 873–878. MR 1563457, http://dx.doi.org/10.1090/S0002-9904-1936-06455-4
• [1] G. Faber Über Tschebyscheffsche Polynome, J. Reine Angew. Math. vol. 150 (1920) pp. 79-106.
• [1] M. Fekete Über einen Satz des Herrn Serge Bernstein, J. Reine Angew. Math. vol. 146 (1916) pp. 88-94.
• [1] Dunham Jackson, The theory of approximation, American Mathematical Society Colloquium Publications, vol. 11, American Mathematical Society, Providence, RI, 1994. Reprint of the 1930 original. MR 1451140 (98a:01022)
• [1] C. de la Vallée Poussin Leçons sur l'approximation des fonctions d'une variable réelle, Paris, 1919.
• [1] E. Lindelöf Sur un principe général de l'analyse, Acta Societatis Scientiarum Fennicae vol. 46 (1915) No. 4.
• [1] N. Lusin and J. Privaloff Sur l'unicité et la multiplicité de fonctions analytiques, Ann. École Norm. (3) vol. 42 (1925) pp. 143-191.
• [1] P. Montel Sur les polynômes d'approximation, Bull. Soc. Math. France vol. 46 (1919) pp. 151-192.
• [1] G. Pólya and G. Szegö Aufgaben und Lehrsätze aus der Analysis, Berlin, 1925.
• [1] J. Priwaloff, Sur les fonctions conjuguées, Bull. Soc. Math. France 44 (1916), 100–103 (French). MR 1504751
• [2] -Sur certaines propriétés métriques des fonctions analytiques, J. École Polytech. (2) vol. 24 (1924) pp. 77-112.
• [1] Marcel Riesz, Sur les fonctions conjuguées, Math. Z. 27 (1928), no. 1, 218–244 (French). MR 1544909, http://dx.doi.org/10.1007/BF01171098
• [1] A. C. Schaeffer and G. Szegö, Inequalities for harmonic polynomials in two and three dimensions, Trans. Amer. Math. Soc. 50 (1941), 187–225. MR 0005164 (3,111b), http://dx.doi.org/10.1090/S0002-9947-1941-0005164-7
• [1] W. Seidel, Über die Ränderzuordnung bei konformen Abbildungen, Math. Ann. 104 (1931), no. 1, 182–243 (German). MR 1512661, http://dx.doi.org/10.1007/BF01457932
• [1] W. E. Sewell, Degree of Approximation by Polynomials in the Complex Domain, Annals of Mathematical Studies, no. 9, Princeton University Press, Princeton, N. J., 1942. MR 0007054 (4,78c)
• [1] V. Smirnoff Sur les formules de Cauchy et de Green et quelques problèmes qui s'y rattachent, Bull. Acad. Sci. URSS. Sér. Math. vol. 7 (1932) pp. 337-371.
• [1] Gabriel Szegő, Über trigonometrische und harmonische Polynome, Math. Ann. 79 (1919), no. 4, 323–339 (German). MR 1511934, http://dx.doi.org/10.1007/BF01498414
• [2] -Über einen Satz des Herrn Serge Bernstein, Schriften der Königsberger Gelehrten Gesellschaft, Naturwissenschaftliche Klasse vol. 5 (1928) pp. 59-70.
• [1] Masatsugu Tsuji, On the Green’s function, Jap. J. Math. 18 (1942), 379–383. MR 0017813 (8,203h)
• [1] J. L. Walsh, On the degree of approximation to a harmonic function, Bull. Amer. Math. Soc. 33 (1927), no. 5, 591–598. MR 1561424, http://dx.doi.org/10.1090/S0002-9904-1927-04416-0
• [2] -Über die Entwicklung einer harmonischen Funktion nach harmonischen Polynomen, J. Reine Angew. Math. vol. 159 (1928) pp. 197-209.
• [3] J. L. Walsh, The approximation of harmonic functions by harmonic polynomials and by harmonic rational functions, Bull. Amer. Math. Soc. 35 (1929), no. 4, 499–544. MR 1561772, http://dx.doi.org/10.1090/S0002-9904-1929-04753-0
• [4] -Interpolation and approximation by rational functions in the complex domain, Amer. Math. Soc. Colloquium Publications, vol. 20, New York, 1935.
• [5] J. L. Walsh, Maximal convergence of sequences of harmonic polynomials, Ann. of Math. (2) 38 (1937), no. 2, 321–354. MR 1503339, http://dx.doi.org/10.2307/1968557
• [1] J. L. Walsh and W. E. Sewell, Sufficient conditions for various degrees of approximation by polynomials, Duke Math. J. 6 (1940), 658–705. MR 0002592 (2,80c)
• [2] J. L. Walsh and W. E. Sewell, Note on the relation between continuity and degree of polynomial approximation in the complex domain, Bull. Amer. Math. Soc. 43 (1937), no. 8, 557–563. MR 1563586, http://dx.doi.org/10.1090/S0002-9904-1937-06603-1
• [3] J. L. Walsh and W. E. Sewell, Note on degree of trigonometric and polynomial approximation to an analytic function, Bull. Amer. Math. Soc. 44 (1938), no. 12, 865–873. MR 1563892, http://dx.doi.org/10.1090/S0002-9904-1938-06893-0
• [4] J. L. Walsh and W. E. Sewell, On the degree of polynomial approximation to analytic functions: problem 𝛽, Trans. Amer. Math. Soc. 49 (1941), 229–257. MR 0003818 (2,276h), http://dx.doi.org/10.1090/S0002-9947-1941-0003818-X
• [1] Stefan Warschawski, Bemerkung zu meiner Arbeit: Über das Randverhalten der Ableitung der Abbildungsfunktion bei konformer Abbildung, Math. Z. 38 (1934), no. 1, 669–683 (German). MR 1545475, http://dx.doi.org/10.1007/BF01170662
• [1] A. Zygmund Trigonometrical series, Monografje Matematyczne, vol. V, Warsaw-Lwów, 1935.
• [2] A. Zygmund, Smooth functions, Duke Math. J. 12 (1945), 47–76. MR 0012691 (7,60b)

Bibliography

[1]

T. Carleman Über die Fourierkoeffizienten einer stetigen Funktion, Acta Math. vol. 41 (1918) pp. 377-384. MR 1555157

[1]

M. L. Cartwright On analytic functions regular in the unit circle, Quart. J. Math. Oxford Ser. vol. 4 (1933) pp. 246-257.

[1]

John Curtiss A note on the degree of polynomial approximation, Bull. Amer. Math. Soc. vol. 42 (1936) pp. 873-878. MR 1563457

[1]

G. Faber Über Tschebyscheffsche Polynome, J. Reine Angew. Math. vol. 150 (1920) pp. 79-106.

[1]

M. Fekete Über einen Satz des Herrn Serge Bernstein, J. Reine Angew. Math. vol. 146 (1916) pp. 88-94.

[1]

D. Jackson The theory of approximation, Amer. Math. Soc. Colloquium Publications, vol. 11, New York, 1930. MR 1451140 (98a:01022)

[1]

C. de la Vallée Poussin Leçons sur l'approximation des fonctions d'une variable réelle, Paris, 1919.

[1]

E. Lindelöf Sur un principe général de l'analyse, Acta Societatis Scientiarum Fennicae vol. 46 (1915) No. 4.

[1]

N. Lusin and J. Privaloff Sur l'unicité et la multiplicité de fonctions analytiques, Ann. École Norm. (3) vol. 42 (1925) pp. 143-191.

[1]

P. Montel Sur les polynômes d'approximation, Bull. Soc. Math. France vol. 46 (1919) pp. 151-192.

[1]

G. Pólya and G. Szegö Aufgaben und Lehrsätze aus der Analysis, Berlin, 1925.

[1]

J. Privaloff Sur les fonctions conjuguées, Bull. Soc. Math. France vol. 44 (1916) pp. 100-103. MR 1504751

[2]

-Sur certaines propriétés métriques des fonctions analytiques, J. École Polytech. (2) vol. 24 (1924) pp. 77-112.

[1]

M. Riesz Sur les fonctions conjuguées, Math. Zeit. vol. 27 (1928) pp. 218-244. MR 1544909

[1]

A. C. Schaeffer and G. Szegö Inequalities for harmonic polynomials in two and three dimensions, Trans. Amer. Math. Soc. vol. 50 (1941) pp. 187-225. MR 0005164 (3:111b)

[1]

W. Seidel Über die Ränderzuordnung bei konformen Abbildungen, Math. Ann. vol. 104 (1931) pp. 182-243. MR 1512661

[1]

W. E. Sewell Degree of approximation by polynomials in the complex domain, Annals of Mathematics Studies, vol. 9, Princeton, 1942. MR 0007054 (4:78c)

[1]

V. Smirnoff Sur les formules de Cauchy et de Green et quelques problèmes qui s'y rattachent, Bull. Acad. Sci. URSS. Sér. Math. vol. 7 (1932) pp. 337-371.

[1]

G. Szegö Über trigonometrische und harmonische Polynome, Math. Ann. vol. 79 (1919) pp. 323-329. MR 1511934

[2]

-Über einen Satz des Herrn Serge Bernstein, Schriften der Königsberger Gelehrten Gesellschaft, Naturwissenschaftliche Klasse vol. 5 (1928) pp. 59-70.

[1]

M. Tsuji On the Green's function, Jap. J. Math. vol. 18 (1941-1943) pp. 379-383. MR 0017813 (8:203h)

[1]

J. L. Walsh On the degree of approximation to a harmonic function, Bull. Amer. Math. Soc. vol. 33 (1927) pp. 591-598. MR 1561424

[2]

-Über die Entwicklung einer harmonischen Funktion nach harmonischen Polynomen, J. Reine Angew. Math. vol. 159 (1928) pp. 197-209.

[3]

-The approximation of harmonic functions by harmonic polynomials and by harmonic rational functions, Bull. Amer. Math. Soc. vol. 35 (1929) pp. 499-544. MR 1561772

[4]

-Interpolation and approximation by rational functions in the complex domain, Amer. Math. Soc. Colloquium Publications, vol. 20, New York, 1935.

[5]

-Maximal convergence of sequences of harmonic polynomials, Ann. of Math. vol. 38 (1937) pp. 321-354. MR 1503339

[1]

J. L. Walsh and W. E. Sewell Sufficient conditions for various degrees of approximation by polynomials, Duke Math. J. vol. 6 (1940) pp. 658-705. MR 0002592 (2:80c)

[2]

-A note on the relation between continuity and degree of polynomial approximation in the complex domain, Bull. Amer. Math. Soc. vol. 43 (1937) pp. 557-563. MR 1563586

[3]

-Note on degree of trigonometric and polynomial approximation to an analytic function, ibid. vol. 44 (1938) pp. 865-873. MR 1563892

[4]

-On the degree of polynomial approximation to analytic functions: Problem , Trans. Amer. Math. Soc. vol. 49 (1941) pp. 229-257. MR 0003818 (2:276h)

[1]

S. E. Warschawski Bemerkung zu meiner Arbeit: Über das Randverhalten der Ableitung der Abbildungsfunktion bei konformer Abbildung, Math. Zeit. vol. 38 (1934) pp. 669-683. MR 1545475

[1]

A. Zygmund Trigonometrical series, Monografje Matematyczne, vol. V, Warsaw-Lwów, 1935.

[2]

-Smooth functions, Duke Math. J. vol. 12 (1945) pp. 47-76. MR 0012691 (7:60b)