Extreme harmonic functions and boundary value problems

Kohur Gowrisankaran

Annales de l'institut Fourier (1963)

  • Volume: 13, Issue: 2, page 307-356
  • ISSN: 0373-0956

How to cite

top

Gowrisankaran, Kohur. "Extreme harmonic functions and boundary value problems." Annales de l'institut Fourier 13.2 (1963): 307-356. <http://eudml.org/doc/73809>.

@article{Gowrisankaran1963,
author = {Gowrisankaran, Kohur},
journal = {Annales de l'institut Fourier},
keywords = {partial differential equations},
language = {eng},
number = {2},
pages = {307-356},
publisher = {Association des Annales de l'Institut Fourier},
title = {Extreme harmonic functions and boundary value problems},
url = {http://eudml.org/doc/73809},
volume = {13},
year = {1963},
}

TY - JOUR
AU - Gowrisankaran, Kohur
TI - Extreme harmonic functions and boundary value problems
JO - Annales de l'institut Fourier
PY - 1963
PB - Association des Annales de l'Institut Fourier
VL - 13
IS - 2
SP - 307
EP - 356
LA - eng
KW - partial differential equations
UR - http://eudml.org/doc/73809
ER -

References

top
  1. [1] H. BAUER, Weiterführung einer axiomatischen Potentialtheorie ohne Kern (Existenz von Potentialen). Z. Wahrscheinlichkeitstheorie 1963, 1, 197-229. Zbl0216.10301MR27 #5926
  2. [2] M. BRELOT, Sur le principe des singularités positives et la topologie de R. S. Martin, Annales Univ. Grenoble Math. Phys., 23, 1948, 113-138. Zbl0030.25601MR10,192b
  3. [3] M. BRELOT, Topology of R. S. Martin and Green Lines, Lectures on functions of a complex variable, Michigan Univ. Press, 1955, 105-121. Zbl0068.06101MR16,1108c
  4. [4] M. BRELOT, Le problème de Dirichlet avec la frontière de Martin, C. R. Ac. Sc., 240, 1955, 142. Zbl0064.09901MR16,923d
  5. [5] M. BRELOT, Le problème de Dirichlet. Axiomatique et frontière de Martin, Journal de Math., 35, 1956, 297-335. Zbl0071.10001MR20 #6607
  6. [6] M. BRELOT, Lectures on Potential Theory. Tata Institute of Fundamental Research, Bombay, 1960. Zbl0098.06903MR22 #9749
  7. [7] M. BRELOT, Séminaire de Théorie du Potentiel, I et II, 1957-1958. 
  8. [8] M. BRELOT and J. L. DOOB, Limites fines et limites angulaires, these Annales 13, 1963. Zbl0132.33902MR33 #4299
  9. [9] G. CHOQUET, Existence et unicité des représentations intégrales au moyen des points extremaux dans les cônes convexes, Seminaire Bourbaki, 130, December, 1956. Zbl0121.09204MR18,219b
  10. [10] G. CHOQUET and P. A. MEYER, Annales Inst. Fourier, t. 13, 1963, 138-154. Zbl0122.34602
  11. [11] J. L. DOOB, Conditional Brownian motion and Boundary limits of harmonic functions, Bull. Soc. Math. France, 85, 1957, 431-458. Zbl0097.34004MR22 #844
  12. [12] J. L. DOOB, A non probabilistic proof of the relative Fatou Theorem, Annales Inst. Fourier, t. 9, 1959, 295. Zbl0095.08203MR22 #8233
  13. [13] J. L. DOOB, Discrete Potential Theory and Boundaries, Journal of Maths. and Mechanics, 8, 1959, p. 433-458. Zbl0101.11503MR21 #5825
  14. [13 bis] J. L. DOOB : A relativized Fatou Theorem, Proc. Nat. Ac. Sc. vol. 45 p. 215 (1959). Zbl0106.07801MR21 #5822
  15. [14] P. FATOU, Séries trigonométriques et Séries de Taylor, Acta Mathematica, 30, 1906, 335-400. JFM37.0283.01
  16. [15] K. GOWRISANKARAN, Limites fines "à la frontière" dans la théorie axiomatique du potentiel de M. Brelot, C. R. Ac. Sc., 255, 1962, 450. Zbl0114.30703MR27 #335
  17. [16] K. GOWRISANKARAN, Limites fines et problème de Dirichlet en théorie axiomatique des fonctions harmoniques. C. R. Ac. Sc., 256, 1963, 357. Zbl0114.30704MR26 #5174
  18. [17] R. M. HERVÉ, Recherches Axiomatiques sur la théorie des fonctions surharmoniques et du potentiel, Annales Inst. Fourier, 12, 1962, 415-571. Zbl0101.08103MR25 #3186
  19. [18] L. H. LOOMIS, Introduction to Abstract Harmonic Analysis, von Nostrand Publication. Zbl0052.11701
  20. [19] R. S. MARTIN, Minimal Positive Harmonic Functions, Trans. Amer. Math. Soc., 49, 1941, 137-172. Zbl0025.33302MR2,292hJFM67.0343.03
  21. [20] MYSKIS, On the concept of a boundary. Mat. Sbornik N. S. 25 (67) 387-414 (1949), Amer, Math. Soc. Translations series 1, vol. 8 p. 11. Zbl0039.18802
  22. [21] L. NAÏM, Sur le rôle de la frontière de R. S. Martin dans la théorie du potentiel, Annales Inst. Fourier, t. 7, 1957, 183-285. Zbl0086.30603MR20 #6608

Citations in EuDML Documents

top
  1. Daniel Sibony, Allure à la frontière minimale d'une classe de transformations. Théorème de Doob généralisé
  2. Kohur Gowrisankaran, Fatou-Naïm-Doob limit theorems in the axiomatic system of Brelot
  3. Daniel Sibony, Théorème de limites fines et problème de Dirichlet
  4. Kohur Gowrisankaran, Multiply superharmonic functions
  5. Kohur Gowrisankaran, On minimal positive harmonic functions
  6. Howard Lawrence Jackson, Some results on thin sets in a half plane
  7. J. L. Doob, Some classical function theory theorems and their modern versions
  8. Peter Loeb, An axiomatic treatment of pairs of elliptic differential equations
  9. Marcel Brelot, Étude comparée des deux types d'effilement
  10. Tosiaki Kori, La théorie des espaces fonctionnels à nullité 1 et le problème de Neumann sur les espaces harmoniques

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.