Geodesic
Properties of Bernstein Functions of Several Complex Variables
Matematičeskie zametki, Tome 93 (2013) no. 2, pp. 216-226

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A multidimensional generalization of the class of Bernstein functions is introduced and the properties of functions belonging to this class are studied. In particular, a new proof of the integral representation of Bernstein functions of several variables is given. Examples are considered.
Keywords: Bernstein function of several variables, absolutely monotone function, integral representation, Markov process. 
A. R. Mirotin. Properties of Bernstein Functions of Several Complex Variables. Matematičeskie zametki, Tome 93 (2013) no. 2, pp. 216-226. http://geodesic.mathdoc.fr/item/MZM_2013_93_2_a6/
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[1] C. Berg, J. P. R. Christensen, P. Ressel, Harmonic Analysis on Semigroups. Theory of Positive Definite and Related Functions, Grad. Texts in Math., 100, Springer-Verlag, Berlin, 1982 | MR | Zbl

[2] V. Feller, Vvedenie v teoriyu veroyatnostei i ee prilozheniya, T. 2, Mir, M., 1984 | MR | Zbl

[3] D. Applebaum, “Lévy processes – from probability to finance and quantum groups”, Notices Amer. Math. Soc., 51:11 (2004), 1336–1347 | MR | Zbl

[4] C. Berg, K. Boyadzhiev, R. deLaubenfelse, “Generation of generators of holomorphic semigroups”, J. Austral. Math. Soc. Ser. A, 55:2 (1993), 246–269 | DOI | MR | Zbl

[5] A. R. Mirotin, “Deistvie funktsii klassa Shenberga $\mathscr T$ na konuse dissipativnykh elementov banakhovoi algebry”, Matem. zametki, 61:4 (1997), 630–633 | DOI | MR | Zbl

[6] A. R. Mirotin, “Funktsii klassa Shenberga $\mathscr T$ deistvuyut v konuse dissipativnykh elementov banakhovoi algebry. II”, Matem. zametki, 64:3 (1998), 423–430 | DOI | MR | Zbl

[7] A. R. Mirotin, “Mnogomernoe $\mathscr T$-ischislenie ot generatorov $C_0$-polugrupp”, Algebra i analiz, 11:2 (1999), 142–169 | MR | Zbl

[8] N. I. Akhiezer, Klassicheskaya problema momentov i nekotorye voprosy analiza, svyazannye s neyu, Fizmatgiz, M., 1961 | MR | Zbl

[9] N. Burbaki, Integrirovanie. Mery na lokalno kompaktnykh prostranstvakh. Prodolzhenie mery. Integrirovanie mer. Mery na otdelimykh prostranstvakh, Elementy matematiki, Nauka, M., 1977

[10] M. Markl, S. Shnider, J. Stasheff, Operads in Algebra, Topology and Physics, Math. Surveys Monogr., 96, Amer. Math. Soc., Providence, RI, 2002 | MR | Zbl

[11] B. V. Shabat, Vvedenie v kompleksnyi analiz. Ch. 2. Funktsii neskolkikh peremennykh, Nauka, M., 1976 | MR | Zbl

[12] A. B. Goncharov, “The classical trilogarithm, algebraic $K$-theory of fields and Dedekind zeta functions”, Bull. Amer. Math. Soc. (N.S.), 24:1 (1991), 155–162 | DOI | MR | Zbl

[13] E. Khille, R. Fillips, Funktsionalnyi analiz i polugruppy, IL, M., 1962 | MR | Zbl

[14] A. R. Mirotin, “Vpolne monotonnye funktsii na polugruppakh Li”, Ukr. matem. zhurn., 52:6 (2000), 841–845 | MR | Zbl