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李育嘉 Yuh-Jia Lee

Yuh-Jia Lee Title Chair Professor
Phone (07)5919170
Fax (07)5919344
E-Mail yjlee@nuk.edu.tw
Homepage 機率講義Ch1、Ch2、Ch3、Ch4、Ch5、Ch6.pdf
Lecture on White Noise Analysis.pdf
Office Room 412,College of Science
  Education 國立成功大學數學系學士
國立清華大學數學碩士
美國紐約州立大學（水牛城分校）數學博士		 top
Employment

國立高雄大學副校長
國立高雄大學教務長
國立高雄大學學務長
國立成功大學數學系教授兼主任
國立成功大學理學院院長
曾獲國科會傑出研究獎
曾獲中山學術著作獎
榮獲中華民國數學會學會獎
國科會自然處數學審議委員(1997~1999，2001~2003，2007-2009)
國科會自然處數學學門諮議委員（1988~1992）
國科會數學門規劃委員招集人 (1998-1999年)
教育部國中小九年一貫數學領域新綱要推動計畫南二區招集
教育部中華民國參加亞太暨國際數學奧林匹亞競賽工作小組員(1986-1999)
教育部中華民國參加數學奧林匹亞競賽觀察員 (2000)
中央研究院數學研究所學術詢委員（2000～2004）
中華民國數學會理事長（1998-1999）
中華民國數學會理事、監事(1985--)
美國數學會Mathematical Review評論員（1971迄今）

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Research fields 機率、泛函分析、微分方程 top
Research introduction top
Journal papers
  1. Yuh-Jia Lee and Shin-Hung Shih (2006). Le vy white noise on infinite dimensional spaces: Existence and characterization of mesurable support,J.Funct. Anal. In Press . SCI
  2. Yuh-Jia Lee and Shin-Hung Shih (2004). Analysis of Levy white noise functionals, J. Funct. Anal., In press.
  3. Yuh-Jia Lee and Chen-Yuh Shih (2003). Analysis of generalized Levy functionals, J. Funct. Anal., In press.
  4. Yuh-Jia Lee and Chen-Yuh Shih (2003). The product formula of multiple Levy-Ito integral, Bull. Math. Acad. Sinica, to appear
  5. Yuh-Jia Lee and Chen-Yuh Shih (2002). The Riesz representation theorem on infinite dimensional spaces and its applications, Infinite Dimensional Analysis, Quantum Probability and Related Topics, 5, No.1, 41-59
  6. Yuh-Jia Lee and Shin-Hung Shih (2002). Clark formula of generalized Wiener functionals, Quantum Information IV, 127-146, World Scientific
  7. Yuh-Jia Lee and Chen-Yuh Shih (2001). A probabilistuc approach to the integral representation of positive white noise functionals, Stochastic Analysis and Applications, 19, No.2, 215-234. 計畫編號：NSC-88-2115-M-006 –006 CMP 1 817 620
  8. Yuh-Jia Lee (2001). Heisenberg uncertainty principle on abstract Wiener spaces, J. Korea Math. Soc., 38, No.2, 283-296.
  9. Yuh-Jia Lee and Shin-Hung Shih (2000). Donsker's delta function of Levy process, Acta Applicandae Mathematicae, 63 219-231~CMP~1~834~220
  10. Yuh-Jia Lee and Shin-Hung Shih (2000). Ito's formula for Levy functionals, Quantum Information II, 87-105, World Scientific.
  11. Yuh-Jia Lee, H. H. Kuo and C. Y. Shih (2000). Wiener-Ito Theorem in terms of Wick tensors,Acta Applicandae Mathematicae, 63, 203-218 CMP~1!834~219
  12. Yuh-Jia Lee and Shin-Hung Shih (1999). The Segal-Bargmann transform for Levy functional, J. Func. Anal., 168, 46-83~MR~2001c: 60107
  13. Yuh-Jia Lee and Aurel Stan (1999). An infinite dimensional Heisenberg uncertainty principle, Taiwaness J. Math. 3, No.4, 529-538 MR~2001a: 28016
  14. Yuh-Jia Lee (1998). Generalized white noise functionals on classical Wiener spaces, J. Korea Math. Soc., 35, No.3, 613--635. 計畫編號：NSC-87-2115-M-006 –001 ~MR 99m: 60087
  15. Yuh-Jia Lee (1997). A generalization of the Riesz representation theorem to infinite dimensions, J. Funct. Analysis, 151, 121-137.計畫編號：NSC-86-2115-M-006 –001 ~MR~99b:46056
  16. Yuh-Jia Lee (1995). Integral representation of second quantization and its application in white noise analysis, J. Func. Anal., 133, 253-276. 計畫編號：NSC-84-2121-M-006 -019~MR~96m:60147
  17. Yuh-Jia Lee (1994). T. S. Chiang and Y. Chow, Exact formulas of certain functionals on Wiener spaces, Stochastic and stochastic reports, 50, 211-223. ~MR~2001e: 60077
  18. Yuh-Jia Lee (1994). Transformation of white noise functionals and applications, In Stochastic Analysis on Infinite Dimensional Spaces, Pitman Research Notes in Mathematics Series 310, 183-196. ~MR~97k: 60222
  19. Yuh-Jia Lee, I. Doku, H. H. Kuo (1994). Fourier transform and heat equation in white noise analysis, In Stochastic Analysis on Infinite Dimensional Spaces, Pitman Research Notes in Mathematics Series 310, 60-74. MR~97k: 60109
  20. Yuh-Jia Lee (1993). Tansformation and Wiener-Ito decomposition of white noise functionals, Bull. Inst. Math. Acad. Sinica, 21, 279-291. MR~95f: 60075
  21. Yuh-Jia Lee (1991). Analytic version of test functionals, Fourier-transform and a characterization of measure in white noise calculus, J. Funct. Anal., 100, 359-380.~MR~92k:60186
  22. Yuh-Jia Lee (1989). Generalized functions on infinite dimensional spaces and its application to white noise calculus, J. Funct. Anal. 82, 429-464. ~MR~90k: 60125
  23. Yuh-Jia Lee (1989). On the convergence of Wiener-Ito decomposition, Bull. Inst. Math. Acad. Sinica. 17, 305-312.~MR~91k:60009
  24. Yuh-Jia Lee (1987). Unitary operators on the space of -functions over abstract Wiener spaces, Soochow J. Math., 13, 165-174. ~MR~89h: 47045
  25. Yuh-Jia Lee (1987). Sharp inequalities and regularity of heat semigroup on infinite dimensional spaces, J. Funct. Anal., 71, 69-87. MR~88f: 28011
  26. Yuh-Jia Lee (1987). T. S. Chiang and Y. Chow, A formula for , Proc. Amer. Math. Soc., 100, 721-724.~MR~88m:60010
  27. Yuh-Jia Lee (1986). Wiener process and Hardy spaces on abstract Wiener spaces, Proc. NSC., Part A, 10, 275-280.
  28. Yuh-Jia Lee (1982). Integral transforms of analytic functions on abstract Wiener spaces, J. Funct. Anal., 47, 153-164.~MR~84j:28021
  29. Yuh-Jia Lee (1981). Fundamental solutions for differential equations associated with the number operator, Trans. Amer. Math. Soc., 268, 467-476; MR~84k: 35140a A correction and some additions, Trans. Amer. Math. Soc., 276(1983), 621-623. ~MR~84k: 35140b
  30. Yuh-Jia Lee (1981). Applications of the Fourier-Wiener transform to differential equations on infinite dimensional spaces, II, J. Diff. Equa., 41, 59-86. ~MR~84a35283
  31. Yuh-Jia Lee (1981). Parabolic equations on infinite dimensional spaces, Bull. Inst. Acad. Sinica, 9, 279-292. ~MR~84d: 35143
  32. Yuh-Jia Lee (1980). Applications of the Fourier-Wiener transform to differential equations on infinite dimensional spaces, I, Trans. Amer. Math. Soc., 262, 262-283.~MR~82k:35098
  33. Yuh-Jia Lee and H. C. Wang (1973). Homomorphism of —Algebras, Chinese J. Math., 1, 189-192.~MR~52 #1171
  34. Yuh-Jia Lee and H. C. Wang (1973). Complex homomorphisms of homogeneous Banach algebras, Tamkang J. Math., 4, 29-33. ~MR~49 #1007
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Conference papers
  1. Analysis of complex Brownian functionals .（中菲雙邊會議, 2007.10.25-27，菲律賓）
  2. Stochastic Analysis (1).（Analysis Seminar & a Mini Course on Stochastic Analysis，台東大學應用數學系，2007.4.28~29）
  3. Stochastic Analysis (2).（Analysis Seminar & a Mini Course on Stochastic Analysis，台東大學應用數學系，2007.4.28~29）
  4. Stochastic Analysis (3).（Analysis Seminar & a Mini Course on Stochastic Analysis，台東大學應用數學系，2007.4.28~29）
  5. Levy White Noise Measures on Infinite Dimensional Spaces.（2006 International Congress of Mathematicians，2006.8.20~9.1，西班牙）
  6. Numerical Simulation of Different-Sized Quantum Dot Array. (7th World Congress on Computational Mechanics, Los Angeles, USA, 2006.7.16~22)
  7. Levy White Noise Measure on Infinite Dimension.（國際分析及應用研討會，2006.5.22-26，泰國曼谷Chulalongkoun University）
  8. Yuh-Jia Lee and T. Z. Huang (2001). Ito formula of Brownian bridge on classical Wiener spaces, Proccedings of the International Conference on Stochastic Analysis, Hammamet, Tunisia.
  9. Yuh-Jia Lee and Chen-Yuh Shih (2000). The Riesz representation theorem on infinite dimensional spaces and its applications, Proceedings of the Third Sino-Philippine Symposium in Analysis (Quezon City) Matimys Mat. Special Issue, 111-121. CMP~1~827~908
  10. Yuh-Jia Lee and Chun-Fu Liu (1996). A Generalization of Mehler Transform, Proceedings of the International Mathematics Conference '94, Kaohsiung, Taiwan, Edited by Y. Fong, W. J. Huang, Y. J. Lee and N. C. Wong. World Scientific. ~MR~98h: 46041
  11. Yuh-Jia Lee (1985). Differential equations associated with the number operator on abstract Wiener Spaces, Proceedings of seminar on differential equations, Chao-Tung University, Hsinchu, Taiwan, 176-191.
  12. Yuh-Jia Lee (1984). Regularity of the Green's operator on abstract Wiener spaces, Symp. Summer '84, Math. Res. Center Reports, 545-561.
  13. Yuh-Jia Lee (1983). Integral transform of —functions over abstract Wiener spaces, Symp. Summer '83, Math. Res. Center Reports, 215-234.
  14. Yuh-Jia Lee (1982). Some regularity properties of abstract Wiener measure, Symp. Summer'82, Math. Res. Center Reports, 51-66.
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Monograph
  1. Yuh-Jia Lee and T. Z. Huang (2004). Ito formula of Brownian bridge on
    classical Wiener spaces, Proccedings of the International Conference on
    Stochastic Analysis and App;lications, Hammamet, Tunisia held in Oct. 20-27,
    2001, Edited by S. Albeverio, Ann B. de Monvel and H. Ouerdiane, p.107-127,Kluwer Academic Publishers. MR2112636
  2. Yuh-Jia Lee and Shin-Hung Shih (2005). A quantum decomposition of Levy
    processes, In “Stochastic Analysis: Classical and Quantum”, edited by T. Hida, World Scientific (2005), 86-99.
  3. Yuh-Jia Lee and Shin-Hung Shih (2004). A characterization of generalized Le
    vy white noise functiponals, In “Quantum information and complexity”, Edited by T. Hida, K, Saito and Si Si,World Siocentific(2004), 321-339
  4. Yuh-Jia Lee and Shin-Hung Shih (2002). Clark formula of generalized Wiener
    functionals, Quantum Information IV, 127-146,World Scientific. MR1947563.
  5. Yuh-Jia Lee and Shih, Cheng-Yuh (2002). The Riesz representation theorem oninfinite dimensional spaces and its applications, Proceedings of the Third
    Sino-Philippine Symposium in Analysis (Quezon City,) Matimys Mat. Special
    Issue, 111-121. MR1827908
  6. Yuh-Jia Lee and Shin-Hung Shih (2000). Convergence of Fock expansion and
    transformations of Brownian functionals, in Functional analysis and Global
    analysis, Edited by T. Sunada and P.W. Sy, 142-156, Springer. 計畫編號：
    NSC-85-2121-M-006 -011~MR~99m:60066
  7. Yuh-Jia Lee (2000). Ito's formula for Levy functionals, Quantum Information II,87-105,World Scientific. MR1880131
  8. Yuh-Jia Lee, Convergence of Fock expansion and transformations of Brownian functionals, in Functional analysis and Global analysis, Edited by T. Sunada and P.W. Sy, 142-156, Springer (1997). （計畫編號：NSC-85-2121-M-006 –011）
  9. Yuh-Jia Lee, Positive generalized functions on infinite dimensional spaces, In Stochastic Process, A Festschrift in Honour of Gopinath Kallianpur, 225-234, Springer-Verlag (1993).
  10. Yuh-Jia Lee, A characterization of generalized functions on infinite dimensional spaces and Bargmann-Segal analytic functions, In Gaussian Random Fields, Series In Probability and Statistics, Vol.1, 272-284, World Scientific (1991).
  11. Yuh-Jia Lee, A reformulation of white noise calculus, in White Noise Analysis-Mathematics and Applications, Edited by T. Hida, H. H. Kuo, J. Potthoff and Streit, 274-293, World Scientific (1990)
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Other publications
  1. Yuh-Jia Lee and Shin-Hung Shih, Calculus of generalized Levy functionals, Preprint.
  2. Yuh-Jia Lee, T. S. Chiang and Y. Chow, Evaluation of certain functional integrals, IMA Preprint Series N0. 245, Univ. of Minnesota (1986).
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Projects  
計畫名稱 執行期限 經費（元） 補助單位
無限微空間上的隨機分析與應用(3/1) 97.08.01-100.07.31 1,289,000
國科會
無窮維空間之分析與量子機率之研究II (3-3) 96.08.01-97.07.31 1,077,000
國科會
無窮維空間之分析與量子機率之研究II (3-2)
95.08.01-96.07.31
678,000
國科會
無窮維空間之分析與量子機率之研究II (3-1)
94.08.01-95.07.31
582,000
國科會
無窮維空間之分析與量子機率之研究 (3-3)
93.08.01-94.07.31
598,400
國科會
無窮維空間之分析與量子機率之研究(3-2)
92.08.01-93.07.31
575,700
國科會
無窮維空間之分析與量子機率之研究(1/3)
91.08.01-92.07.31
665,600
國科會
LEVY泛函之分析與應用(3/3)
90.08.01-91.07.31
421,200
國科會
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Talks
  1. 近代數學的發展趨勢（國立台東大學數學系邀請演講，2006.12.22）
  2. Support Properties of Levy White Noise Measure. (International Conference on Analysis and Random Phenomena. Hammamet, Tunisia, 2005.9.12~17) (invited speaker)
  3. International Conference on Analysis and Random Phenomena, Hammamet, Tunisia, Sept.10-17, 2005, (invited speaker)
  4. International Conference on Stochastic Analysis, Classical and Quantum—Prospective of White Noise Analysis'', Meijo University, Nagoya, Nov. 1-5, 2004 (invited speaker)
  5. Conference on Analysis and Partial Differential Equation, NTHU. Jan.9-11,2004(Plenary speaker)
  6. 九十二年度中華民國數學年會及數學學術研討會，12月19日至21日，中央大學(invited speaker)
  7. Volterra-CIRM-Greifswald International Conference on “Classical and Quantum Levy Processes:Analysis and Applications, Sep. 27-Oct. 13, 2003 Levico, Trento, Italy (invited speaker)
  8. International Conference on Stochastic Analysis and Its Applications, Oct. 19-25, 2003, Hammamet, Tunisia(invited speaker)
  9. Segal-Bargmann transform of Levy functionals. （中山大學應用數學系邀請演講，2002.11.21）
  10. The Fifth International Conference on Quantum Information, March 22-25, 2002, meijo University, Nagoya, Japan(Plenary speaker)
  11. International Conference on Stochastic Analysis and ItsApplications, Oct. 20-28, 2001, Hammamet, Tunisia(invited speaker)
  12. The Fourth International Conference on Quantum Information, Feb-27-March1, 2001, Meijo University, Nagoya, Japan(invited speaker)
  13. Ito formula of Brownian bridge on classical Wiener spaces（Proceedings of the International Conference on Stochastic Analysis, Hammamet, Tunisia., 2001）
  14. Analysis on Infinite Dimensional Spaces(in Honor of Leonard Gross), Jan.10-Jan.13,2001, New Orleans,USA.
  15. Analysis on Infinite Dimensional Space (in Honor of Professor Leonard Gross), Jan. 10-13,2000, New Orleans, USA(invited speaker)
  16. International Conference on Feynman Integrals and Related Topics, July 12-14, 1999, Yonsei University, Seoul, Korea (invited speaker)
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PH.D. students  
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Master students  
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