Harmonic functions and mean value theorems
Časopis pro pěstování matematiky (1975)
- Volume: 100, Issue: 4, page 391-409
- ISSN: 0528-2195
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topNetuka, Ivan. "Harmonické funkce a věty o průměru." Časopis pro pěstování matematiky 100.4 (1975): 391-409. <http://eudml.org/doc/21259>.
@article{Netuka1975,
author = {Netuka, Ivan},
journal = {Časopis pro pěstování matematiky},
language = {cze},
number = {4},
pages = {391-409},
publisher = {Mathematical Institute of the Czechoslovak Academy of Sciences},
title = {Harmonické funkce a věty o průměru},
url = {http://eudml.org/doc/21259},
volume = {100},
year = {1975},
}
TY - JOUR
AU - Netuka, Ivan
TI - Harmonické funkce a věty o průměru
JO - Časopis pro pěstování matematiky
PY - 1975
PB - Mathematical Institute of the Czechoslovak Academy of Sciences
VL - 100
IS - 4
SP - 391
EP - 409
LA - cze
UR - http://eudml.org/doc/21259
ER -
References
top- M. A. Ackoglu R. W. Sharpe, Ergodic theory and boundaries, Trans. Amer. Math. Soc. 1320968, 447-460. MR0224770
- J. Aczél H. Haruki M. A. McKiernan G. N. Sakovič, General and regular solutions of functional equations characterizing harmonic polynomials, Aequationes Math. I (1968), 37-53. (1968) MR0279471
- S. Alinhac, Une caractérisation des fonctions harmoniques dans un ouvert borné par des properiétés de moyenne sur certaines boules, C R. Acad. Sci. Paris, Sér. A-B 275 (1972), 29-31. (1972) MR0306527
- J. R. Baxter, Restricted mean values and harmonie functions, Trans. Amer. Math. Soc. 167 (1972), 451-463. (1972) MR0293112
- E. F. Beckenbach M. Reade, Mean values and harmonie polynomials, Trans. Amer. Math. Soc. 53 (1943), 230-238. (1943) MR0007831
- W. Blaschke, Ein Mittelwertsatz und eine kennzeichnende Eigenschaft des logaritmischen Potentials, Ber. Ver. Sachs. Akad. Wiss. Leipzig 68 (1916), 3-7. (1916)
- A. K. Bose, Functions satisfying a weighted average property, Trans. Amer. Math. Soc. 118 (1965), 472-487. (1965) Zbl0136.09404MR0177128
- J. Bramble L. E. Payne, Mean value theorems for polyharmonic functions, Amer. Math. Monthly 73 (1966), 124-127. (1966) MR0192074
- M. Brelot, Éléments de la théorie classique du potential, CDU, Paris, 1969. (1969)
- W. Bródel, Funktionen mit Gaussischen Mittelwerteigenschaften fur konvexe Kurven und Bereiche, , Deutsche Math. 4 (1939), 3-15. (1939)
- A. Brunel, Propriété restreinte de valeur moyenne caractérisant les fonctions harmoniques bornées sur un ouvert , (selon D. Heath et L. Orey), Exposé No. XIV, Séminaire Goulaouic-Schwartz, Paris, 1971-72. (1971)
- Z. Cisielski Z. Semadeni, Przegla̧d niektórych nowszych metod w teorii potenejalu III, Prace matematyezne II (1967), 99-128. (1967)
- R. Courant D. Hilbert, Mathematical methods of Physics, vol. II, Interscience Pub., New York, 1966. (1966)
- I. Černý, Základy analysy v komplexním oboru, Academia, Praha, 1967. (1967) MR0222257
- J. Delsarte, Note sur une propriété nouvelle des fonctions harmoniques, C. R. Acad. Sci. Paris, Sér. A-B 246 (1958), 1358-1360. (1958) Zbl0084.09403MR0096050
- J. Delsarte J. L. Lions, Moyennes generalises, Comment. Math. Helv. 33 (1959), 59-69. (1959) MR0102672
- J. Delsarte, Lectures on topics in mean periodic functions and the two-radius theorem, Tata Inst. Fund. Research, Bombay, 1961. (1961)
- J. Deny, Families fondamentales. Noyaux associes, Ann. Inst. Fourier 3 (1951), 73-101. (1951) MR0067262
- Encyklopadie der mathematischen Wissenschaften, II. Band, 3.L, Teubner-Verlag, 1899-916.
- B. Epstein, On the mean value property of harmonic functions, Proc. Amer. Math. Soc. 13 (1962), 830. (1962) Zbl0109.07501MR0140700
- B. Epstein M. M. Schiffer, On the mean-value property of harmonic functions, J. Analyse Math. 14 (1965), 109-111. (1965) MR0177124
- G. C. Evans, On potentials of positive mass, Trans. Amer. Math. Soc. 37 (1935), 226-253. (1935) Zbl0011.21201MR1501785
- W. Feller, Boundaries induced by non-negative matrices, Trans. Amer. Math. Soc. 83 (1956), 19-54. (1956) Zbl0071.34901MR0090927
- L. Flatto, Functions with a mean value property, J. Math. Mech. 10 (1961), 11-18. (1961) Zbl0097.30605MR0136751
- L. Flatto, The converse of Gauss's theorem for harmonic functions, J. Differential Equations 1 (1965), 483-490. (1965) Zbl0132.07804MR0185134
- A. Friedman W. Littman, Bodies for which harmonic functions satisfy the mean value property, Trans. Amer. Math. Soc. 102 (1962), 147-166. (1962) MR0151627
- A. Friedman W. Littman, Functions satisfying the mean value property, Trans. Amer. Math. Soc. 102 (1962), 167-180. (1962) MR0151628
- W. Fulks, An approximate Gauss mean value theorem, Pac. J. Math. 14 (1964), 513-516. (1964) Zbl0163.34503MR0162047
- A. M. Garsia, A note on the mean value property, Trans. Amer. Math. Soc. 102 (1962), 181-186. (1962) Zbl0103.32202MR0151629
- C. F. Gauss, Algemeine Lehrsatze in Beziehung auf die im verkehrtem Verhaltnisse des Quadrats der Entfernung Wirkenden Anziehungs- und Abstossungs-Krafte, 1840, Werke, 5. Band, Gottingen, 1867.
- R. Godement, Une generalisation du theoreme de la moyenne pour les fonctions harmoniques, C R. Acad. Sci. Paris Ser. A-B 234 (1952), 2137-2139. (1952) Zbl0049.30301MR0047056
- M. Goldstein W. H. Ow, On the mean-value property of harmonic functions, Proc. Amer. Math. Soc. 29 (1971), 341-344 MR0279320
- J. W. Green, Mean values of harmonic functions on homothetic curves, Pac. J. Math. 6 (1956), 279-282. (1956) Zbl0071.32003MR0080759
- M. Heins, Complex function theory, Academic Press, New York, 1968. (1968) Zbl0155.11501MR0239054
- L. L. Helms, Introduction to potential theory, Wiley-Interscience, New York, 1969. (1969) Zbl0188.17203MR0261018
- M. R. Hirschfeld, Sur les fonctions -harmoniques dans un espace localement compact mesuré, C R. Acad. Sci. Paris, Ser. A-B 262 (1966), 174-176. (1966) MR0192069
- E. Hopf, Bemerkungen zur Aufgabe 49, Jber. Deutsch. Math. Verein. 39 (1930), 2. Teil, 5-7. (1930)
- F. Huckemann, On the one circle problem for harmonic functions, J. London Math. Soc. 29 (1954), 491-497. (1954) Zbl0056.32601MR0063499
- G. Choquet J. Deny, Sur quelques propriétés de moyenne caractéristiques des fonctions harmoniques et polyharmoniques, Bull. Soc. Math. France 12 (1944), 118-140. (1944) MR0013496
- V. Jarnik, Diferencialní počet II, NCSAV, Praha, 1956. (1956)
- F. John, Plane waves and spherical means applied to partial differential equations, Interscience Publishers, New York, 1955. (1955) Zbl0067.32101MR0075429
- O. D. Kellog, Converses of Gauss's theorem on the arithmetic mean, Trans. Amer. Math. Soc. 36 (1934), 227-242. (1934) MR1501739
- C. D. Kellog, Les moyennes arithmetiques dans la theorie du potentiel, L'Enseignement Math. 21 (1928), 14-26. (1928)
- O. D. Kellog, Foundations of Potential Theory, Springer-Verlag, Berlin, 1967. (1967) MR0222317
- J. Král I. Netuka J. Veselý, Teorie potenciálu II, SPN, Praha, 1972. (1972)
- P. Koebe, Herleitung der partiellen Differentialgleichungen der Potentialfunktion aus deren Integraleigenschaft, Sitzungsber. Berlin. Math. Gessellschaft 5 (1906), 39-42. (1906)
- Ü. Kuran, On the mean value property of harmonic functions, Bull. London Math. Soc. 4(1972), 311-312. (1972) Zbl0257.31006MR0320348
- H. Lebesgue, Sur le théoreme de la moyenne de Gauss, Bull. Soc. Math. France 40 (1912), 16-17. (1912)
- E. Levi, Sopra una proprietá caratteristica delle funzione armoniche, Atti della Reale Acad. Lincei 18(1909), 10-15. (1909)
- J. L. Littlewood, On the definition of a subharmonic function, J. London Math. Soc. 2 (1927), 189-192. (1927)
- J. L. Littlewood, Some problems in real and complex analysis, Hath. Math. Monographs, Massachusetts, 1968. (1968) Zbl0185.11502
- J. Mařík, Úloha č. 10, Časopis Pěst. Mat. 81 (1956), 470. (1956)
- J. Mařík, Dirichletova úloha, Časopis Pěst. Mat. 82 (1957), 257-282. (1957) MR0090666
- L Netuka, Řešení úlohy č. 10, Časopis Pěst. Mat. 94 (1969), 223-225. (1969)
- M. Parreau, Sur les moyennes des fonctions harmoniques et analytiques et la classification des surfaces de Riemann, Ann. Inst. Fourier 3 (1951), 103-197. (1951) Zbl0047.32004MR0050023
- M. Plancherel, Les problěmes de Cantor et de du Bois-Reymond, Ann. Sci. Ecole Norm. Sup. 31 (1914), 223-262. (1914) MR1509177
- H. Poritsky, On operations permutable with the Laplacian, Amer. J. Math. 54 (1932), 667-691. (1932) Zbl0005.36001MR1506929
- H. Poritsky, Generalizations of the Gauss law of spherical mean, Trans. Amer. Math. Soc. 43 (1938), 199-225. (1938) MR1501939
- I. Privaloff, On a theorem of S. Saks, Mat. Sb. 9 (51) (1941), 457-460. (1941) Zbl0024.40402MR0004364
- S. Saks, On the operators Blaschke and Privaloff for subharmonic functions, Mat. Sb. 9(51)(1941), 451-456. (1941) MR0004363
- S. Saks A. Zykmund, Analytic functions, PWN, Warszawa, 1965. (1965)
- K. T. Smith, Mean values and continuty of Riesz potentials, Comm. Pure Appl. Math. 9 (1956), 569-576. (1956) MR0081357
- E. Smyrnélis, Sur les moyennes des fonctions paraboliques, Bull. Sci. Math. 93 (1969), 163-173. (1969) MR0277901
- E. Smyrnélis, Mesures normales et fonctions harmoniques, Bull. Sci. Math. 95 (1971), 197-207. (1971) MR0294681
- J. M. Thompson, Distribution of mass for averages of Newtonian potential functions, Bull. Amer. Math. Soc. 41 (1935), 744-752. (1935) Zbl0013.01501MR1563179
- L. Tonelli, Sopra una proprietá caratteristica delle funzione armoniche, Atti della Reale Acad. Lincei 18 (1909), 557-532. (1909)
- W. A. Veech, A zero - one law for a class of random walks and a converse to Gauss mean value theorem, Ann. of Math. 97 (1973), 189-216. (1973) Zbl0282.60048MR0310269
- W. A. Veech, A converse to the mean value theorem for harmonic functions, (preprint). Zbl0324.31002
- V. Volterra, Alcune osservazioni sopra proprietá atte ad individuare una funzione, Atti della Reale Acad. Lincei 18 (1909), 263-266. (1909)
- J. L. Walsh, A mean value theorem for polynomials and harmonic polynomials, Bull. Amer. Math. Soc. 42 (1936), 923-930. (1936) Zbl0016.12302MR1563465
- L. Zalcman, Analyticity and the Pompeiue problem, Arch. Rational Mech. Anal. 47 (1972), 237-254. (1972) MR0348084
- L. Zalcman, Mean values and differential equations, Israel J. Math. 14 (1973), 339-353. (1973) Zbl0263.35013MR0335835
- S. Zaremba, Contributions á la théorie d'une equation fonctionnelle de la physique, Rend. Circ. Mat. Palermo (1905), 140. (1905)
- S. Alinhac, Une caracterisation des fonctions harmoniques dans un ouvert par certaines propriétés de moyenne, Rev. Roumaine Math. Pures Appl. 18 (1973), 1465-1472. (1973) MR0346169
- S. C. Chu, On a mean value property for solutions of a wave equation, Amer. Math. Monthly 74 (1967), 711-713. (1967) Zbl0149.06402MR0212419
- M. Nicolescu, Une propriété caractéristique de moyenne des solutions régulières de l'équation de la chaleur, Com. Acad. R. P. Romane 2 (1952), 677-679. (1952) Zbl0082.31001MR0070844
- M. Nicolescu, Sur une propriété caractéristique de moyenne des fonctions polycaloriques, Com. Acad. R. P. Romane 4 (1954), 551-554. (1954) Zbl0059.09201MR0070845
- M. Nicolescu, Propriété de moyenne des fonctions harmoniques bornées dans un demi-plan ou dans un angle droit, Rev. Roumaine Math. Pures Appl. 1 (1956), 43-50. (1956) MR0083046
- M. Nicolescu, Sur les moyennes généralisées successives d'une fonction, Rev. Roumaine Math. Pures Appl. 6 (1961), 429-441; Mathematica (Cluj) 4 (27) (1962), 107-121. (1961) Zbl0108.05203MR0155987
- D. P. Stanford, Functions satisfying a mean value property at their zeros, Amer. Math. Monthly 80 (1973), 665-667. (1973) Zbl0277.26006MR0315068
- J. Barta, Some mean value theorems in the potential theory, Acta Tech. Acad. Sci. Hungar. 75(1973), 3-11. (1973) Zbl0309.31006MR0348129
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