Joseph Fels Ritt
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- Bull. Amer. Math. Soc. 57 (1951), 307-318
References
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A. Joseph Fels Ritt, Differential equations from the algebraic standpoint, Amer. Math. Soc. Colloquium Publications, vol. 14, 1932, 173 pp.
- J. F. Ritt, Theory of Functions, King’s Crown Press, New York, 1947. MR 0021970, DOI 10.7312/ritt94362
- Joseph Fels Ritt, Integration in Finite Terms. Liouville’s Theory of Elementary Methods, Columbia University Press, New York, N. Y., 1948. MR 0024949, DOI 10.7312/ritt91596
- Joseph Fels Ritt, Differential Algebra, American Mathematical Society Colloquium Publications, Vol. XXXIII, American Mathematical Society, New York, N. Y., 1950. MR 0035763, DOI 10.1090/coll/033 1. Joseph Fels Ritt, A control for least square solutions, Astronomical Journal vol. 28 (1913) pp. 73-74. 2. Joseph Fels Ritt, Note sur la fonction sin [(n+1) arc cos x], Nouvelles Annales de Mathématiques vol. 14 (1914) pp. 184-186.
- J. F. Ritt, On certain real solutions of Babbage’s functional equation, Ann. of Math. (2) 17 (1916), no. 3, 113–122. MR 1503574, DOI 10.2307/2007270 4. Joseph Fels Ritt, On the derivatives of a function at a point, Ann. of Math. vol. 18 (1916) pp. 18-23.
- J. F. Ritt, The resolution into partial fractions of the reciprocal of an entire function of genus zero, Trans. Amer. Math. Soc. 18 (1917), no. 1, 21–26. MR 1501059, DOI 10.1090/S0002-9947-1917-1501059-4 6.Joseph Fels Ritt, On the differentiability of asymptotic series, Bull. Amer. Math. Soc. vol. 24 (1918) pp. 225-227. 7. Joseph Fels Ritt, Sur L’itération des fonctions rationelles, C. R. Acad. Sci. Paris vol. 166 (1918) pp. 380-381.
- J. F. Ritt, On the differentiability of the solution of a differential equation with respect to a parameter, Ann. of Math. (2) 20 (1919), no. 4, 289–291. MR 1502564, DOI 10.2307/1967123
- J. F. Ritt, On the iteration of rational functions, Trans. Amer. Math. Soc. 21 (1920), no. 3, 348–356. MR 1501149, DOI 10.1090/S0002-9947-1920-1501149-6 10. Joseph Fels Ritt, On weighting factor curves in flat fire, Journal of United States Artillery vol. 53 (1920) pp. 404-410.
- J. F. Ritt, On the conformal mapping of a region into a part of itself, Ann. of Math. (2) 22 (1921), no. 3, 157–160. MR 1502580, DOI 10.2307/1967437 12. Joseph Fels Ritt, Note on equal continuity, Bull. Amer. Math. Soc. vol. 27 (1921) pp. 351-353.
- J. F. Ritt, Periodic functions with a multiplication theorem, Trans. Amer. Math. Soc. 23 (1922), no. 1, 16–25. MR 1501186, DOI 10.1090/S0002-9947-1922-1501186-3
- J. F. Ritt, Prime and composite polynomials, Trans. Amer. Math. Soc. 23 (1922), no. 1, 51–66. MR 1501189, DOI 10.1090/S0002-9947-1922-1501189-9
- J. F. Ritt, On algebraic functions which can be expressed in terms of radicals, Trans. Amer. Math. Soc. 24 (1922), no. 1, 21–30. MR 1501211, DOI 10.1090/S0002-9947-1922-1501211-X 16. Joseph Fels Ritt, Sur les fonctions rationnelles permutables, C. R. Acad. Sci. Paris vol. 176 (1923) pp. 60-68.
- J. F. Ritt, On the integrals of elementary functions, Trans. Amer. Math. Soc. 25 (1923), no. 2, 211–222. MR 1501240, DOI 10.1090/S0002-9947-1923-1501240-7
- J. F. Ritt, Permutable rational functions, Trans. Amer. Math. Soc. 25 (1923), no. 3, 399–448. MR 1501252, DOI 10.1090/S0002-9947-1923-1501252-3
- J. F. Ritt, Equivalent rational substitutions, Trans. Amer. Math. Soc. 26 (1924), no. 2, 221–229. MR 1501274, DOI 10.1090/S0002-9947-1924-1501274-3 20. Joseph Fels Ritt, Analytic functions and periodicity, Bull. Amer. Math. Soc. vol. 30 (1924) pp. 406-409. 21. Joseph Fels Ritt, Note on the Dirichlet series with complex exponents, Ann. of Math. vol. 26 (1924) p. 144.
- J. F. Ritt, Elementary functions and their inverses, Trans. Amer. Math. Soc. 27 (1925), no. 1, 68–90. MR 1501299, DOI 10.1090/S0002-9947-1925-1501299-9
- J. F. Ritt, New proofs of two well known theorems on quadratic forms, Ann. of Math. (2) 26 (1925), no. 3, 202–204. MR 1502689, DOI 10.2307/1967897 24. Joseph Fels Ritt, Sur les fonctions méromorphes qui admettent un theorème d’addition ou de multiplication, C. R. Acad. Sci. Paris vol. 182 (1926) pp. 201-202. 25. Joseph Fels Ritt, Simplification de la méthode de Liouville dans la théorie des fonctions élémentaires, C. R. Acad. Sci. Paris, vol. 183 (1926) pp. 331-332.
- J. F. Ritt, Transcendental transcendency of certain functions of Poincaré, Math. Ann. 95 (1926), no. 1, 671–682. MR 1512299, DOI 10.1007/BF01206632 27. Joseph Fels Ritt, On the integration in finite terms of linear differential equations of the second order, Bull. Amer. Math. Soc. vol. 33 (1927) pp. 51-57.
- Joseph Fels Ritt, Differential Algebra, American Mathematical Society Colloquium Publications, Vol. XXXIII, American Mathematical Society, New York, N. Y., 1950. MR 0035763, DOI 10.1090/coll/033
- J. F. Ritt, Meromorphic functions with addition or multiplication theorems, Trans. Amer. Math. Soc. 29 (1927), no. 2, 341–360. MR 1501392, DOI 10.1090/S0002-9947-1927-1501392-2
- J. F. Ritt, Real functions with algebraic addition theorems, Trans. Amer. Math. Soc. 29 (1927), no. 2, 361–368. MR 1501393, DOI 10.1090/S0002-9947-1927-1501393-4
- J. F. Ritt, A factorization theory for functions $\sum _{i=1}^na_ie^{\alpha _ix}$, Trans. Amer. Math. Soc. 29 (1927), no. 3, 584–596. MR 1501406, DOI 10.1090/S0002-9947-1927-1501406-X
- J. F. Ritt, On Certain Points in the Theory of Dirichlet Series, Amer. J. Math. 50 (1928), no. 1, 73–86. MR 1506655, DOI 10.2307/2370849 33. Joseph Fels Ritt, Calculus, differential and integral, Encyclopedia Britannica 14th ed., vol. 4, 1929, pp. 555-558.
- J. F. Ritt, Algebraic combinations of exponentials, Trans. Amer. Math. Soc. 31 (1929), no. 4, 654–679. MR 1501505, DOI 10.1090/S0002-9947-1929-1501505-4
- J. F. Ritt, On the zeros of exponential polynomials, Trans. Amer. Math. Soc. 31 (1929), no. 4, 680–686. MR 1501506, DOI 10.1090/S0002-9947-1929-1501506-6
- J. F. Ritt, On a certain ring of functions of two variables, Trans. Amer. Math. Soc. 32 (1930), no. 2, 155–170. MR 1501531, DOI 10.1090/S0002-9947-1930-1501531-3
- J. F. Ritt, Manifolds of functions defined by systems of algebraic differential equations, Trans. Amer. Math. Soc. 32 (1930), no. 4, 569–599. MR 1501554, DOI 10.1090/S0002-9947-1930-1501554-4
- J. F. Ritt, Representation of analytic functions as infinite products, Math. Z. 32 (1930), no. 1, 1–3. MR 1545149, DOI 10.1007/BF01194617 39. Joseph Fels Ritt, Systems of algebraic differential equations, Proc. Nat. Acad. Sci. U.S.A. vol. 17 (1931) pp. 366-368. 40. Joseph Fels Ritt, Integral functions obtained by compounding polynomials, Bull. Amer. Math. Soc. vol. 39 (1933) pp. 627-632. 41. Joseph Fels Ritt, (With J. L. Doob) Systems of algebraic difference equations, Amer.J. Math.vol. 55 (1933) pp. 505-514. 42. Joseph Fels Ritt, Algebraic difference equations, Bull. Amer. Math. Soc. vol. 40 (1934) pp. 303-308.
- J. F. Ritt, Systems of algebraic differential equations, Ann. of Math. (2) 36 (1935), no. 2, 293–302. MR 1503223, DOI 10.2307/1968571
- J. F. Ritt, Jacobi’s problem on the order of a system of differential equations, Ann. of Math. (2) 36 (1935), no. 2, 303–312. MR 1503224, DOI 10.2307/1968572
- J. F. Ritt, Indeterminate expressions involving a function and its derivatives, Monatsh. Math. Phys. 43 (1936), no. 1, 97–104. MR 1550514, DOI 10.1007/BF01707591
- J. F. Ritt, On the singular solutions of algebraic differential equations, Ann. of Math. (2) 37 (1936), no. 3, 552–617. MR 1503299, DOI 10.2307/1968478
- J. F. Ritt, On Certain Points in the Theory of Algebraic Differential Equations, Amer. J. Math. 60 (1938), no. 1, 1–43. MR 1507300, DOI 10.2307/2371541
- J. F. Ritt, Systems of Differential Equations. I. Theory of Ideal, Amer. J. Math. 60 (1938), no. 3, 535–548. MR 1507334, DOI 10.2307/2371594 49. Joseph Fels Ritt, Algebraic aspects of the theory of differential equations, Amer. Math. Soc. Semicentennial Publications, vol. 2, 1938, pp. 35-55. 50. Joseph Fels Ritt, On ideals of differential polynomials, Proc. Nat. Acad. Sci. U.S.A. vol. 25 (1939) pp. 90-91. 51. Joseph Fels Ritt, On the intersections of algebraic differential manifolds, Proc. Nat. Acad. Sci. U.S.A. vol. 25 (1939) pp. 214-215.
- J. F. Ritt and H. W. Raudenbush Jr., Ideal theory and algebraic difference equations, Trans. Amer. Math. Soc. 46 (1939), 445–452. MR 605, DOI 10.1090/S0002-9947-1939-0000605-4
- J. F. Ritt and E. R. Kolchin, On certain ideals of differential polynomials, Bull. Amer. Math. Soc. 45 (1939), 895–898. MR 606, DOI 10.1090/S0002-9904-1939-07112-7
- J. F. Ritt, On the intersections of irreducible components in the manifold of a differential polynomial, Proc. Nat. Acad. Sci. U.S.A. 26 (1940), 354–356. MR 2440, DOI 10.1073/pnas.26.5.354
- J. F. Ritt, On a type of algebraic differential manifold, Trans. Amer. Math. Soc. 48 (1940), 542–552. MR 3306, DOI 10.1090/S0002-9947-1940-0003306-X
- J. F. Ritt, Complete difference ideals, Amer. J. Math. 63 (1941), 681–690. MR 6165, DOI 10.2307/2371611 57. Joseph Fels Ritt, Bezout’s theorem and algebraic differential equations, Trans. Amer. Math. Soc. vol. 53 (1943) pp. 74-82.
- J. F. Ritt, A family of functions and its theory of contact, Bull. Amer. Math. Soc. 49 (1943), 109–113. MR 8246, DOI 10.1090/S0002-9904-1943-07862-7 59. Joseph Fels Ritt, On the manifolds of partial differential polynomials, Ann. of Math. vol. 46 (1945) pp. 102-112.
- J. F. Ritt, Analytical theory of singular solutions of partial differential equations of the first order, Ann. of Math. (2) 46 (1945), 120–143. MR 13189, DOI 10.2307/1969152
- J. F. Ritt, On the singular solutions of certain differential equations of the second order, Proc. Nat. Acad. Sci. U.S.A. 32 (1946), 255–258. MR 17828, DOI 10.1073/pnas.32.10.255
- J. F. Ritt, Abel’s theorem and a generalization of one-parameter groups, Trans. Amer. Math. Soc. 67 (1949), 491–497. MR 32765, DOI 10.1090/S0002-9947-1949-0032765-X
- Joseph Fels Ritt, Differential Algebra, American Mathematical Society Colloquium Publications, Vol. XXXIII, American Mathematical Society, New York, N. Y., 1950. MR 0035763, DOI 10.1090/coll/033
- J. F. Ritt, Differential groups and formal Lie theory for an infinite number of parameters, Ann. of Math. (2) 52 (1950), 708–726. MR 37308, DOI 10.2307/1969444 65. Joseph Fels Ritt, Differential groups of order two, Ann. of Math., unpublished. 66. Joseph Fels Ritt, Subgroups of differential groups, Ann. of Math., unpublished. 67. Joseph Fels Ritt, Differential groups, Proceedings of the International Congress, Harvard, 1950, unpublished.
Additional Information
- Journal: Bull. Amer. Math. Soc. 57 (1951), 307-318
- DOI: https://doi.org/10.1090/S0002-9904-1951-09529-4
- MathSciNet review: 0041789