Book Review
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MathSciNet review:
1566968
Full text of review:
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Book Information:
Authors:
Aurel Cornea and
Gabriela Licea
Title:
Order and potential resolvent families of kernels
Additional book information:
Lecture Notes in Mathematics, no. 494, Springer-Verlag, Berlin, Heidelberg, New York, 1975, 154 pp., $7.40.
Henri Cartan and Jacques Deny, Le principe du maximum en théorie du potentiel et la notion de fonction surharmonique, Acta Sci. Math. (Szeged) 12 (1950), 81–100 (French). MR 37411
Jacques Deny, Familles fondamentales. Noyaux associés, Ann. Inst. Fourier (Grenoble) 3 (1951), 73–101 (1952) (French). MR 67262
J. L. Doob, Semimartingales and subharmonic functions, Trans. Amer. Math. Soc. 77 (1954), 86–121. MR 64347, DOI 10.1090/S0002-9947-1954-0064347-X
J. L. Doob, A probability approach to the heat equation, Trans. Amer. Math. Soc. 80 (1955), 216–280. MR 79376, DOI 10.1090/S0002-9947-1955-0079376-0
G. A. Hunt, Markoff processes and potentials. I, II, Illinois J. Math. 1 (1957), 44–93, 316–369. MR 91349
Georges Lion, Familles d’opérateurs et frontières en théorie du potentiel, Ann. Inst. Fourier (Grenoble) 16 (1966), no. fasc. 2, 389–453 (French). MR 215366
Gabriel Mokobodzki, Densité relative de deux potentiels comparables, Séminaire de Probabilités, IV (Univ. Strasbourg, 1968/69) Lecture Notes in Math., Vol. 124, Springer, Berlin, 1970, pp. 170–194 (French). MR 0294679
Gabriel Mokobodzki, Quelques propriétés remarquables des opérateurs presque positifs, Séminaire de Probabilités, IV (Univ. Strasbourg, 1968/69) Lecture Notes in Math., Vol. 124, Springer, Berlin, 1970, pp. 195–207 (French). MR 0294680
Gabriel Mokobodzki, Dualité formelle et représentation intégrale des fonctions excessives, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 531–535. MR 0419809
Daniel Ray, Resolvents, transition functions, and strongly Markovian processes, Ann. of Math. (2) 70 (1959), 43–72. MR 107302, DOI 10.2307/1969891
Daniel W. Stroock, The Kac approach to potential theory. I, J. Math. Mech. 16 (1967), 829–852. MR 0208690
- 1.
- H. Cartan and J. Deny, Le principe du maximum en théorie du potentiel et la notion de fonction surharmonique, Acta Sci. Math. Szeged 12 (1950), 81-100. MR 12, 257. MR 0037411
- 2.
- J. Deny, Familles fondamentales. Noyaux associés, Ann. Inst. Fourier (Grenoble) 3 (1951), 73-101 (1952). MR 16, 698. MR 67262
- 3.
- J. L. Doob, Semimartingales and subharmonic functions. Trans. Amer. Math. Soc. 77 (1954), 86-121. MR 16, 269. MR 64347
- 4.
- J. L. Doob, A probability approach to the heat equation, Trans. Amer. Math. Soc. 80 (1955), 216-280. MR 18, 76. MR 79376
- 5.
- G. A. Hunt, Markoff processes and potentials. I, Illinois J. Math. 1 (1957), 44-93. MR 19, 951. MR 91349
- 6.
- G. Lion, Familles d'opérateurs et frontière en théorie du potentiel, Ann. Inst. Fourier (Grenoble) 16 (1966), fasc. 2, 389-453. MR 35 #6207. MR 215366
- 7a. G. Mokobodzki, Densité relative de deux potentiels comparables, Séminaire de Probabilités, IV (Univ. Strasbourg, 1968/69), Lecture Notes in Math., vol. 124, Springer-Verlag, Berlin and New York, 1970, pp. 170-194. MR 45 #3747. MR 294679
- 7b. G. Mokobodzki, Quelques propriétés remarquables des opérateurs presque positifs, Séminaire de Probabilités, IV (Univ. Strasbourg, 1968/69), Lecture Notes in Math., vol. 124, Springer-Verlag, Berlin and New York, 1970, pp. 195-207. MR 45 #3748. MR 294680
- 8.
- G. Mokobodzki, Dualité formelle et représentation intégrale des fonctions excessives, Actes Congrès Internat. Math. (Nice, 1970), vol. 2, Gauthier-Villars, Paris, 1971, pp. 531-535. MR 419809
- 9.
- D. Ray, Resolvents, transltion functions, and strongly Markovian processes, Ann. of Math. (2) 70 (1959), 43-72. MR 21 #6027. MR 107302
- 10.
- D. W. Stroock, The Kac approach to potential theory. I, J. Math. Mech. 16 (1967), 829-852. MR 34 #8499. MR 208690
9. D. Ray, Resolvents, transltion functions, and strongly Markovian processes, Ann. of Math. (2) 70 (1959), 43-72. MR 21 #6027.
10. D. W. Stroock, The Kac approach to potential theory. I, J. Math. Mech. 16 (1967), 829-852. MR 34 #8499.
Review Information:
Reviewer:
P. A. Meyer
Journal:
Bull. Amer. Math. Soc.
83 (1977), 672-676
DOI:
https://doi.org/10.1090/S0002-9904-1977-14340-1