메뉴 건너뛰기




Volumn 57, Issue 4, 2008, Pages 1679-1713

On a remarkable semigroup of homomorphisms with respect to free multiplicative convolution

Author keywords

Boolean convolution; Free additive convolution; Free meixner states; Free multiplicative convolution

Indexed keywords


EID: 54049095524     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.2008.57.3285     Document Type: Article
Times cited : (67)

References (23)
  • 1
    • 84875116902 scopus 로고    scopus 로고
    • N. I. AKHIEZER, The Classical Moment Problem and Some Related Questions in Analysis, Translated by N. Kemmer, Hafner Publishing Co., New York, 1965. MR 0184042 (32 #1518)
    • N. I. AKHIEZER, The Classical Moment Problem and Some Related Questions in Analysis, Translated by N. Kemmer, Hafner Publishing Co., New York, 1965. MR 0184042 (32 #1518)
  • 2
    • 2942648262 scopus 로고    scopus 로고
    • M. ANSHELEVICH, Free martingale polynomials, J. Funct. Anal. 201 (2003), 228-261, http://dx.doi.org/10.1016/S0022-1236(03)00061- 2. MR 1986160 (2004f:46079)
    • M. ANSHELEVICH, Free martingale polynomials, J. Funct. Anal. 201 (2003), 228-261, http://dx.doi.org/10.1016/S0022-1236(03)00061- 2. MR 1986160 (2004f:46079)
  • 4
    • 11144340257 scopus 로고    scopus 로고
    • Atoms and regularity for measures in a partially defined free convolution semigroup
    • 20061:46095
    • S. T. BELINSCHI and H. BERCOVICI, Atoms and regularity for measures in a partially defined free convolution semigroup, Math. Z. 248 (2004), 665-674, http://dx.doi.org/10.1007/s00209-004-0671- y. MR 2103535 (20061:46095)
    • (2004) Math. Z , vol.248 , pp. 665-674
    • BELINSCHI, S.T.1    BERCOVICI, H.2
  • 5
    • 15744366679 scopus 로고    scopus 로고
    • Partially defined, semigroups relative to multiplicative free convolution, Int. Math. Res. Not. (2005), 65-101, http://dx.doi.org/10.1155/ IMRN.2005.65. MR2128863 (2006f:46061)
    • Partially defined, semigroups relative to multiplicative free convolution, Int. Math. Res. Not. (2005), 65-101, http://dx.doi.org/10.1155/ IMRN.2005.65. MR2128863 (2006f:46061)
  • 6
    • 84875100016 scopus 로고    scopus 로고
    • Burgers equation in matrix models
    • work in progress
    • S. T. BELINSCHI and A. GUIONNET, Burgers equation in matrix models (work in progress).
    • BELINSCHI, S.T.1    GUIONNET, A.2
  • 7
    • 35448978705 scopus 로고    scopus 로고
    • η-series and a Boolean Bercovici-Pata bijection for bounded k-tuples
    • S. T. BELINSCHI and A. NICA, η-series and a Boolean Bercovici-Pata bijection for bounded k-tuples, Adv. Math. 217 (2008), 1-41, http://dx.doi.org/10.1016/j.aim.2007.06.015. MR 2357321
    • (2008) Adv. Math , vol.217 , pp. 1-41
    • BELINSCHI, S.T.1    NICA, A.2
  • 9
    • 0033464422 scopus 로고    scopus 로고
    • Ann. of Math, 2, With an appendix by Philippe Biane, MR 1709310 2000i:46061
    • H. BERCOVICI and V. PATA, Stable laws and domains of attraction in free probability theory, Ann. of Math. (2) 149 (1999) (With an appendix by Philippe Biane), 1023-1060, http://dx.doi.org/10.2307/ 121080. MR 1709310 (2000i:46061)
    • (1999) Stable laws and domains of attraction in free probability theory , vol.149 , pp. 1023-1060
    • BERCOVICI, H.1    PATA, V.2
  • 10
    • 0001410646 scopus 로고
    • Free convolution of measures with unbounded support
    • MR 125411695c:46109
    • H. BERCOVICI and D. V. VOICULESCU, Free convolution of measures with unbounded support, Indiana Univ. Math. J. 42 (1993), 733-773, http://dx.doi.org/10.1512/iumj.1993.42.42033. MR 1254116(95c:46109)
    • (1993) Indiana Univ. Math. J , vol.42 , pp. 733-773
    • BERCOVICI, H.1    VOICULESCU, D.V.2
  • 12
    • 0001583449 scopus 로고    scopus 로고
    • On the free convolution with a semi-circular distribution
    • 99e:46084
    • P. BIANE, On the free convolution with a semi-circular distribution, Indiana Univ. Math. J. 46 (1997), 705-718, http://dx.doi.org/10.1512/iumj.1997.46.1467. MR 1488333 (99e:46084)
    • (1997) Indiana Univ. Math. J , vol.46 , pp. 705-718
    • BIANE, P.1
  • 13
    • 0032330569 scopus 로고    scopus 로고
    • Processes with free increments
    • 99e:46085
    • Processes with free increments, Math. Z. 227 (1998), 143-174, http://dx.doi.org/10.1007/PL00004363. MR 1605393 (99e:46085)
    • (1998) Math. Z , vol.227 , pp. 143-174
  • 14
    • 0035600164 scopus 로고    scopus 로고
    • Remarks on t-transformations of measures and convolutions
    • http://dx.doi.org/ 10.1016/50246-0203(01)01084-6. MR 1863276 20021:60005, English, with English and French summaries
    • M. BOŻEJKO and J. WYSOCZAŃSKI, Remarks on t-transformations of measures and convolutions, Ann. Inst. H. Poincaré Probab. Statist. 37 (2001), 737-761, http://dx.doi.org/ 10.1016/50246-0203(01)01084-6. MR 1863276 (20021:60005) (English, with English and French summaries)
    • (2001) Ann. Inst. H. Poincaré Probab. Statist , vol.37 , pp. 737-761
    • BOŻEJKO, M.1    WYSOCZAŃSKI, J.2
  • 15
    • 84875115292 scopus 로고    scopus 로고
    • p Spaces, Dover Publications, Inc., 2000.
    • p Spaces, Dover Publications, Inc., 2000.
  • 16
    • 0001457433 scopus 로고
    • Addition of freely independent random variables
    • http://dx.doi.org/10. 1016/0022-1236(92)90055-N. MR 1165862 94g:46069
    • H. MAASSEN, Addition of freely independent random variables, J. Funct. Anal. 106 (1992), 409-438, http://dx.doi.org/10. 1016/0022-1236(92)90055-N. MR 1165862 (94g:46069)
    • (1992) J. Funct. Anal , vol.106 , pp. 409-438
    • MAASSEN, H.1
  • 17
    • 0001009889 scopus 로고    scopus 로고
    • On the multiplication of free N-tuples of noncommutative random variables
    • MR 1400060 981:46069
    • A. NICA and R. SPEICHER, On the multiplication of free N-tuples of noncommutative random variables, Amer. J. Math. 118 (1996), 799-837. MR 1400060 (981:46069)
    • (1996) Amer. J. Math , vol.118 , pp. 799-837
    • NICA, A.1    SPEICHER, R.2
  • 19
    • 0000404789 scopus 로고
    • Addition of certain noncommuting random variables
    • http://dx.doi.org/10. 1016/0022-1236(86)90062-5. MR 839105 87j:46122
    • D. V. VOICULESCU, Addition of certain noncommuting random variables, J. Funct. Anal. 66 (1986), 323-346, http://dx.doi.org/10. 1016/0022-1236(86)90062-5. MR 839105 (87j:46122)
    • (1986) J. Funct. Anal , vol.66 , pp. 323-346
    • VOICULESCU, D.V.1
  • 20
    • 0001465703 scopus 로고
    • Multiplication of certain noncommuting random variables
    • MR 915507 89b:46076
    • Multiplication of certain noncommuting random variables, J. Operator Theory 18 (1987), 223-235. MR 915507 (89b:46076)
    • (1987) J. Operator Theory , vol.18 , pp. 223-235
  • 21
    • 21144462319 scopus 로고
    • The analogues of entropy and of Fisher's information measure in free probability theory. I
    • 94k:46137
    • The analogues of entropy and of Fisher's information measure in free probability theory. I, Comm. Math. Phys. 155 (1993), 71-92, http://dx.doi.org/10.1007/BF02100050. MR 1228526 (94k:46137)
    • (1993) Comm. Math. Phys , vol.155 , pp. 71-92
  • 22
    • 84875106837 scopus 로고    scopus 로고
    • Lectures on free probability theory, Proc. Lectures on Probability Theory and Statistics, Saint-Flour, 1998, Lecture Notes in Math., 1738, Springer, Berlin, 2000, pp. 279-349. MR 1775641 (2001g:46121)
    • Lectures on free probability theory, Proc. Lectures on Probability Theory and Statistics, Saint-Flour, 1998, Lecture Notes in Math., vol. 1738, Springer, Berlin, 2000, pp. 279-349. MR 1775641 (2001g:46121)
  • 23
    • 84875098454 scopus 로고    scopus 로고
    • D. V. VOICULESCU, K. J. DYKEMA, and A. NICA, Free Random Variables, CRM Monograph Series, 1, American Mathematical Society, Providence, RI, 1992, ISBN 0-8218-6999-X, A noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups. MR 1217253 (94c:46133)
    • D. V. VOICULESCU, K. J. DYKEMA, and A. NICA, Free Random Variables, CRM Monograph Series, vol. 1, American Mathematical Society, Providence, RI, 1992, ISBN 0-8218-6999-X, A noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups. MR 1217253 (94c:46133)


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.