Interest

Functional Analysis, Probability Theory, Quantum Probability & Infinite Dimensional Analysis
Operator Theory, (Quantum) White Noise Analysis etc,.

Research articles

1. Heo, Jaeseong; Ji, Un Cig; Kim, Young Yi Covariant representations on Krein C* -modules associated to pairs of two maps. J. Math. Anal. Appl. 398 (2013), no. 1, 35–45. 46L08 (47L30)

2. Ji, Un Cig; Kim, Jae Hee φ -derivations on operators on q -Fock space. J. Math. Phys. 53 (2012), no. 3, 033502, 7 pp. (Reviewer: Michael Frank) 81S05 (81S25)

3. Heo, Jaeseong; Belavkin, Viacheslav P.; Ji, Un Cig Reconstruction theorem for stationary monotone quantum Markov processes. Bull. Korean Math. Soc. 49 (2012), no. 1, 63–74. (Reviewer: Roberto Quezada) 46L89 (46L53 60G10 60J25 81S25)

4. Accardi, Luigi; Barhoumi, Abdessatar; Ji, Un Cig Quantum Laplacians on generalized operators on boson Fock space. Probab. Math. Statist. 31 (2011), no. 2, 203–225. (Reviewer: Nobuhiro Asai)

5. Belavkin, V. P.; Heo, Jaeseong; Ji, Un Cig Quantum white noise analysis and quantum stochastic equations. Quantum probability and related topics, 90–124, QP–PQ: Quantum Probab. White Noise Anal., 27, World Sci. Publ., Hackensack, NJ, 2011. (Reviewer: Adam G. Skalski) 81S25 (46L53 60H40)

6. Ji, Un Cig; Kim, Young Yi Convolutions of white noise operators. Bull. Korean Math. Soc. 48 (2011), no. 5, 1003–1014. (Reviewer: Nobuhiro Asai) 60H40 (46F25)

7. Heo, Jaeseong; Belavkin, Viacheslav P.; Ji, Un Cig Monotone quantum stochastic processes and covariant dynamical hemigroups. J. Funct. Anal. 261 (2011), no. 11, 3345–3365. 81S25 (46L08)

8. Heo, Jaeseong; Ji, Un Cig Quantum stochastic processes for maps on Hilbert C ∗ -modules. J. Math. Phys. 52 (2011), no. 5, 053501, 16 pp. (Reviewer: Michael Frank) 81S25 (46L08)

9. Accardi, Luigi; Ji, Un Cig; Saitô, Kimiaki Exotic Laplacians and derivatives of white noise. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 14 (2011), no. 1, 1–14. 60H40

10. Im, Man Kyu; Ji, Un Cig; Park, Yoon Jung Relations among the first variation, the convolutions and the generalized Fourier-Gauss transforms. Bull. Korean Math. Soc. 48 (2011), no. 2, 291–302. (Reviewer: Jae Gil Choi) 28C20 (44A20 44A35 60J65)

11. Ji, Un Cig; Obata, Nobuaki Quantum white noise derivatives and associated differential equations for white noise operators. Quantum probability and infinite dimensional analysis, 42–54, QP–PQ: Quantum Probab. White Noise Anal., 25, World Sci. Publ., Hackensack, NJ, 2010. (Reviewer: Nobuhiro Asai) 81S25 (46N50 60H40)

12. Ji, Un Cig; Obata, Nobuaki Implementation problem for the canonical commutation relation in terms of quantum white noise derivatives. J. Math. Phys. 51 (2010), no. 12, 123507, 15 pp. (Reviewer: Adam G. Skalski) 81S05 (60H40 81S25)

13. Ji, Un Cig; Sahu, Lingaraj; Sinha, Kalyan B. Characterization of unitary processes with independent increments. Commun. Stoch. Anal. 4 (2010), no. 4, 593–614. (Reviewer: Nicolas Privault) 60G51 (47D06 81S25)

14. Heo, Jaeseong; Ji, Un Cig Radon-Nikodým type theorem for α -completely positive maps. J. Math. Phys. 51 (2010), no. 10, 103505, 10 pp. 46L05

15. Accardi, Luigi; Ji, Un Cig; Saitô, Kimiaki Errata: Exotic Laplacians and associated stochastic processes [Infin. Dimens. Anal. Quantum Probab. Relat. Top., Vol. 12 (2009), no. 1, pp. 1–19] [MR2509982]. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 13 (2010), no. 2, 345. 60H40 (46F25 46N30)

16. Heo, Jaeseong; Hong, Jang Pyo; Ji, Un Cig On KSGNS representations on Krein C ∗ -modules. J. Math. Phys. 51 (2010), no. 5, 053504, 13 pp. (Reviewer: Camillo Trapani) 46L08 (47B50)

17. Ji, Un Cig; Obata, Nobuaki Quantum stochastic gradients. Interdiscip. Inform. Sci. 15 (2009), no. 3, 345–359. (Reviewer: Adam G. Skalski) 81S25 (46F25 46N50 60H05 60H40)

18. Ji, Un Cig; Obata, Nobuaki Quantum stochastic integral representations of Fock space operators. Stochastics 81 (2009), no. 3-4, 367–384. (Reviewer: Dora Seleši) 81S25 (46F25 60H40)

19. Accardi, Luigi; Ji, Un Cig; Saitô, Kimiaki Exotic Laplacians and associated stochastic processes. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 12 (2009), no. 1, 1–19. (Reviewer: Habib Ouerdiane) 60H40 (46F25 46N30)

20. Ji, Un Cig; Obata, Nobuaki Annihilation-derivative, creation-derivative and representation of quantum martingales. Comm. Math. Phys. 286 (2009), no. 2, 751–775. (Reviewer: Michael Skeide) 46L53 (46F25 60H40 81S25)

21. Ji, Un Cig; Obata, Nobuaki Generalized white noise operator fields and quantum white noise derivatives. Analyse et probabilités, 17–33, Sémin. Congr., 16, Soc. Math. France, Paris, 2008. (Reviewer: Nobuhiro Asai) 60H40 (46F25 81S25)

22. Ji, Un Cig Quantum extensions of Fourier-Gauss and Fourier-Mehler transforms. J. Korean Math. Soc. 45 (2008), no. 6, 1785–1801. (Reviewer: Habib Ouerdiane) 46F25 (60H40)

23. Belavkin, Viacheslav; Ji, Un Cig Quantum Itô algebra and quantum martingale. Noncommutative harmonic analysis with applications to probability, 47–58, Banach Center Publ., 78, Polish Acad. Sci. Inst. Math., Warsaw, 2007. (Reviewer: Robin Hudson) 81S25 (46F25 46L53 46N50)

24. Ji, Un Cig; Ouerdiane, Habib; Saitô, Kimiaki Quantum stochastic process associated with quantum Lévy Laplacian. Commun. Stoch. Anal. 1 (2007), no. 2, 231–245. (Reviewer: Adam G. Skalski) 60H40 (46F25 46N50 47D06 81S25)

25. Ji, Un Cig; Kim, Young Yi; Park, Su Hyung Unitary multiplier and dilation of projective isometric representation. J. Math. Anal. Appl. 336 (2007), no. 1, 399–410. (Reviewer: Steven P. Kaliszewski) 46L55 (22D25 47D03)

26. Ji, Un Cig; Obata, Nobuaki; Ouerdiane, Habib Quantum Lévy Laplacian and associated heat equation. J. Funct. Anal. 249 (2007), no. 1, 31–54. (Reviewer: Dora Seleši) 60H40 (35R15 46F25 81S25)

27. Ji, Un Cig; Saitô, Kimiaki A similarity between the Gross Laplacian and the Lévy Laplacian. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 10 (2007), no. 2, 261–276. (Reviewer: Dora Seleši) 60H40 (46F25 46N30)

28. Ji, Un Cig; Min, Byeong Su q -white noise and non-adapted stochastic integral. Quantum probability, 267–275, Banach Center Publ., 73, Polish Acad. Sci. Inst. Math., Warsaw, 2006. (Reviewer: Wided Ayed) 60H40 (33D99 81S05 81S25)

29. Ji, Un Cig Stochastic integral representations of quantum martingales on multiple Fock space. Proc. Indian Acad. Sci. Math. Sci. 116 (2006), no. 4, 489–505. (Reviewer: Michael Skeide) 81S25 (46L53 60G48 60H05)

30. Ji, Un Cig; Sinha, Kalyan B. Uniqueness of integrands in quantum stochastic integral. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 9 (2006), no. 4, 607–616. (Reviewer: Robin Hudson) 81S25 (46N50 60H40)

31. Ji, Un Cig; Obata, Nobuaki Unitarity of generalized Fourier-Gauss transforms. Stoch. Anal. Appl. 24 (2006), no. 4, 733–751. (Reviewer: Mark A. McKibben) 60H40 (46F25 46N30)

32. Ji, Un Cig; Kim, Young Yi On a q -Fock space and its unitary decomposition. Bull. Korean Math. Soc. 43 (2006), no. 1, 53–62. 81S05 (46L60 46N50)

33. Ji, Un Cig Integral representation of Hilbert-Schmidt operators on boson Fock space. Stochastic analysis: classical and quantum, 35–45, World Sci. Publ., Hackensack, NJ, 2005. (Reviewer: Robin Hudson) 81S25 (47B10 47N50)

34. Ji, Un Cig; Obata, Nobuaki Admissible white noise operators and their quantum white noise derivatives. Infinite dimensional harmonic analysis III, 213–232, World Sci. Publ., Hackensack, NJ, 2005. (Reviewer: Habib Ouerdiane) 81S25 (46F25 60H40)

35. Ji, Un Cig; Sinha, Kalyan B. Integral representation of quantum martingales. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 8 (2005), no. 1, 55–72. (Reviewer: Robin Hudson) 81S25 (46F25 46N50 60G48)

36. Ji, Un Cig; Lim, Kyung Pil Fock space operator valued martingale convergence. Proceedings of the International Conference on Stochastic Analysis and Applications, 129–143, Kluwer Acad. Publ., Dordrecht, 2004. (Reviewer: Nobuaki Obata) 81S25 (46F25 46N50 47A70 47N30 60G48 60H40)

37. Ji, Un Cig; Obata, Nobuaki A role of Bargmann-Segal spaces in characterization and expansion of operators on Fock space. J. Math. Soc. Japan 56 (2004), no. 2, 311–338. (Reviewer: Habib Ouerdiane) 46E50 (46F25 46G20 46N50 47A70 60H40 81S25)

38. Ji, Un Cig; Obata, Nobuaki Unitarity of Kuo's Fourier-Mehler transform. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 7 (2004), no. 1, 147–154. 60H40 (46F25)

39. Ji, Un Cig; Obata, Nobuaki A unified characterization theorem in white noise theory. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 6 (2003), no. 2, 167–178. (Reviewer: Jorge A. León) 60H40 (46A32 46F25 46G20)

40. Ji, Un Cig Stochastic integral representation theorem for quantum semimartingales. J. Funct. Anal. 201 (2003), no. 1, 1–29. (Reviewer: Nicolas Privault) 81S25 (60H40)

41. Ji, Un Cig; Obata, Nobuaki Quantum white noise calculus. Non-commutativity, infinite-dimensionality and probability at the crossroads, 143–191, QP–PQ: Quantum Probab. White Noise Anal., 16, World Sci. Publ., River Edge, NJ, 2002. (Reviewer: Habib Ouerdiane) 81S25 (60H40)

42. Ji, Un Cig A characterization of weighted Fock space operators. Trends in infinite-dimensional analysis and quantum probability (Japanese) (Kyoto, 2001). Sūrikaisekikenkyūsho Kōkyūroku No. 1278 (2002), 96–113. 46E99 (60H40)

43. Ji, Un Cig; Obata, Nobuaki Segal-Bargmann transform of white noise operators and white noise differential equations. Analytical study of quantum information and related fields (Japanese) (Kyoto, 2001). Sūrikaisekikenkyūsho Kōkyūroku No. 1266 (2002), 59–81. 60H40 (46N50 81S25)

44. Ji, Un Cig; Obata, Nobuaki; Ouerdiane, Habib Analytic characterization of generalized Fock space operators as two-variable entire functions with growth condition. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 5 (2002), no. 3, 395–407. 60H40 (46E50 47N30)

45. Chung, Dong Myung; Ji, Un Cig; Obata, Nobuaki Quantum stochastic analysis via white noise operators in weighted Fock space. Rev. Math. Phys. 14 (2002), no. 3, 241–272. (Reviewer: Alves O. Bolivar) 60H40 (46F25 46N50 81S25)

46. Chung, Dong Myung; Ji, Un Cig; Saitô, Kimiaki Notes on a C0 -group generated by the Lévy Laplacian. Proc. Amer. Math. Soc. 130 (2002), no. 4, 1197–1206 (electronic). (Reviewer: Isamu Dôku) 35R15 (46F25 46G05 47D06 60H40)

47. Ji, Un Cig Functional Itô formula for quantum semimartingales. Infinite dimensional analysis and quantum probability theory (Japanese) (Kyoto, 2000). Sūrikaisekikenkyūsho Kōkyūroku No. 1227 (2001), 154–169. 81S25 (60H05)

48. Ji, Un Cig Cauchy problems in white noise analysis and an application to finite dimensional PDEs. Quantum information, II (Nagoya, 1999), 71–86, World Sci. Publ., River Edge, NJ, 2000. (Reviewer: Alves O. Bolivar) 60H40 (35K90 46G05)

49. Ji, Un Cig; Obata, Nobuaki Initial value problem for white noise operators and quantum stochastic processes. Infinite dimensional harmonic analysis (Kyoto, 1999), 203–216, Gräbner, Altendorf, 2000. (Reviewer: Jan Ubøe) 60H40 (81S25)

50. Chung, Dong Myung; Ji, Un Cig Poisson equations associated with differential second quantization operators in white noise analysis. Recent developments in infinite-dimensional analysis and quantum probability. Acta Appl. Math. 63 (2000), no. 1-3, 89–100. (Reviewer: Ambar Sengupta) 46F25 (47D99 60H40)

51. Chung, Dong Myung; Ji, Un Cig Multi-parameter transformation groups on white noise functionals. J. Math. Anal. Appl. 252 (2000), no. 2, 729–749. (Reviewer: Nobuaki Obata) 60H40 (46F25)

52. Ji, Un Cig Cauchy problems in white noise analysis and an application to finite dimensional PDEs. II. New developments in infinite-dimensional analysis and quantum probability theory (Japanese) (Kyoto, 1999). Sūrikaisekikenkyūsho Kōkyūroku No. 1139 (2000), 30–42. 60H40 (35R60 46F25 60H15)

53. Chung, Chang-Hoon; Chung, Dong Myung; Ji, Un Cig One-parameter groups and cosine families of operators on white noise functions. J. Korean Math. Soc. 37 (2000), no. 5, 687–705. (Reviewer: Yuh-Jia Lee) 60H40 (35R15 46F25 47D06 47D09)

54. Ji, Un Cig Integral kernel operators on regular generalized white noise functions. Bull. Korean Math. Soc. 37 (2000), no. 3, 601–618. 60H40 (46F25 47B34 47D03)

55. Chung, Dong Myung; Ji, Un Cig; Saitô, Kimiaki Cauchy problems associated with the Lévy Laplacian in white noise analysis. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 2 (1999), no. 1, 131–153. (Reviewer: Sandra Cerrai) 35R15 (35R60 46G05 60H40)

56. Chung, Dong Myung; Chung, Tae Su; Ji, Un Cig A characterization theorem for operators on white noise functionals. J. Math. Soc. Japan 51 (1999), no. 2, 437–447. (Reviewer: Jan Ubøe) 60H40 (46F25 47N30 60G20)

57. Chung, Dong Myung; Ji, Un Cig Some Cauchy problems in white noise analysis and associated semigroups of operators. Stochastic Anal. Appl. 17 (1999), no. 1, 1–22. (Reviewer: Jan Ubøe) 60H25 (35R15 46F25 47D06)

58. Chung, Dong Myung; Ji, Un Cig; Obata, Nobuaki Higher powers of quantum white noises in terms of integral kernel operators. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 1 (1998), no. 4, 533–559. (Reviewer: John E. Gough) 81S25 (46N50)

59. Chung, Dong Myung; Chung, Tae Su; Ji, Un Cig Products of white noise functionals and associated derivations. International Conference on Probability Theory and its Applications (Taejon, 1998). J. Korean Math. Soc. 35 (1998), no. 3, 559–574. 60H40 (46F25 60G20)

60. Chung, Dong Myung; Ji, Un Cig; Obata, Nobuaki Transformations on white noise functions associated with second order differential operators of diagonal type. Nagoya Math. J. 149 (1998), 173–192. (Reviewer: Isamu Dôku) 60H99 (46F25 47B38 60G20)

61. Chung, Dong Myung; Ji, Un Cig Transforms on white noise functionals with their applications to Cauchy problems. Nagoya Math. J. 147 (1997), 1–23. (Reviewer: Isamu Dôku) 60H99 (35R15 46G12 60G20)

62. Chung, Dong Myung; Chung, Tae Su; Ji, Un Cig A simple proof of analytic characterization theorem for operator symbols. Bull. Korean Math. Soc. 34 (1997), no. 3, 421–436. (Reviewer: A. V. Uglanov) 46F25 (46G12)

63. Chung, Dong Myung; Ji, Un Cig Cauchy problems for a partial differential equation in white noise analysis. J. Korean Math. Soc. 33 (1996), no. 2, 309–318. (Reviewer: A. V. Uglanov) 35R15 (46F25 46G12 60H99)