邓冠铁: 二级教授，博士生导师，俄罗斯“UFA Mathematical Jounal”数学杂志编委. 1990.7 任副教授，1994.6 破格晋升为教授. 2002-2009 任www.3659.com分析教研室主任. 曾任“Frontiers of Mathematics in China ” 杂志编委. 申请者到现在已指导博士 20 名, 16 人已毕业获博士学位（其中4人 已成为教授）. 申请者已发表的论文(包括与他人合作论文）有170 篇左右，到2018 年6 月止被美国数学评论MR 检索184篇(其中48 篇为SCI 检索), 数学评论MR 检索申请者论文被引用次数总共有169 次. 邓冠铁主译英文教材”Complex variables and Applications”(Seventh Edition) 一部（约59 万字）2005 年由机械工业出版社出版. 邓冠铁独撰21世纪高等学校研究生教材”复分析”（约28万字）, 2010年2月由 北京师范大学出版社出版. 邓冠铁，张艳慧著的“ 次调和分析”学术专著共16万多字，2015年由科学出版社出版.

对于直线上随时间变化的实可测函数 s(t), 物理中经常称为信号,假设s 平方可积, 通过作s(t)的 Hilbert变换 (Hs)(t) 构造一个复函数(称为解析信号） (As)(t)=s(t)+i(Hs)(t), 它是上半平面某个解析函数的边值, As 在数学上表示为具有非负的Fourier频率的基本信号(或箭谐振动)的(无穷)线性组合. 如果将其写为单一的幅度-相位表 达式 :(As)(t)=A(t)e^{i\varphi (t)} ( A(t)\geq 0 称为解析振幅, \varphi (t) 称为辐角或解析相位), 它的导数\varphi '(t) (如果存在的话)称为(一维)解析瞬时频率(Instantaneous Frequency), 这拟乎暗示瞬时频率应该是非负的，暗示解析信号是平面区域中某个解析函数的边值. 于是在数学理论上, 可以定义直线上的解析信号是平面区域中某个解析函数的边值. 平面图像是二维信号（彩色图像可以看成是六维信号(三种颜色的叠加)）, 图像分析学者试图将二维信号分解为单份量信号之和, 从而可以类似一维的情况分析解析瞬时频率. 对于这种二维(2D) 瞬时频率, 北京大学彭立中教授在10000 个科学难题一书中把``2D" 瞬时频率”作为数学难题提出, 认为``2D" 瞬时频率”还没有建立. 其中用数学中多复变解析函数方法来解决此问题是一个重要思想, 发现解决解析信号中的问题和方法与管状区域 \mathbb{R}^n+iB 上的多元复变量的加权Hardy 空间（或Bergman空间)上的解析函数f(x+iy) 的边界值(当y趋向0时, 或作为广义函数) f(x)有很多的联系,我们应该考虑管状区域上的多元复变量的加权 Hardy 空间的解析函数f(z) 的边界值(或作为广义函数)f(x), 把它看成解析信号, 从而定义一类解析函数的边界值(或在广义函数意义下的)f(x)=|f(x)|e^{i\varphi(x)}, 由此定义解析相位及它的梯度（方向）如果频率简单定义为一个在单位时间内周期振动的度量的话, 那这个定义就比较狭隘了. 我们也知道还有一个量描述频率, 就是角频率.一个质点( 空间向量) 在空间绕一轴旋转得到一个角频率, 这个角频率不但有大小, 还有方向. 如果再假设轴也是变动的, 我们可以得到$``2D"$ 瞬时角频率”和多维“瞬时角频率”, 它们不但有大小, 还有方向(梯度). 这种解析是有数学意义的.

1. 国家自然科学基金面上项目, 11271045, 广义解析信号与华生问题, 2012/01-2016/12, 60万元，已结题，主持

2. 博士学科点专项科研基金项目, 20100003110004，华生问题与函数系的完备性，2011/01-2013/12， 6万元，已结题，主持

3. 留学回国人员科研启动基金项目, 科技字[2002]第015号，华生问题和推广, 2002/06-2005/12, 3万元，已结题，主持

4. 国家自然科学基金面上项目, 10071005, 华生问题和推广，2001/01-2003/12，8万元， 已结题，主持

5. 国家自然科学基金青年项目, 19001024, 复分析及其应用，1991/01-1993/12， 1万元，已结题 ， 主持

6. 国家自然科学基金面上项目, 11071020, 复合材料中的椭圆和抛物方程 , 2011/01-2013/12, 30万元 ， 已结题. 参加者

7. 国家自然科学基金面上项目, 10671022, 与平均曲率有关的非线性椭圆方程 , 2007/01-2009/12, 26万元 ， 已结题. 参加者

8. 国家自然科学基金面上项目, 10371011, 几何中的非线性椭圆方程, 2004/01-2006/12, 26万元, 已结题，参加者

9. 国家自然科学基金面上项目, 19371063, 拟必然分析，维纳-黎曼流形与分布的拉回, 1994/01-1996/12 ,已结题，参加者

主要论文目录 (56篇 SCI)

(1) Guantie Deng(#)(*); Tao Qian, An application of entire function theory to analytic signals , Journal of Mathematical Analysis and Applications, 2012.5.1, 389(1): 54~57 (SCI)

(2) Pei Dang; Guantie Deng(*); Tao Qian, A sharper uncertainty principle , Journal of Functional Analysis, 2013.11.15,265(10): 2239~2266 (SCI)

(3) Yanhui Zhang(*); Guantie Deng; Tao Qian, Integral representations of a class of harmonic functions in the half space , Journal of Differential Equations, 2016, 260(2): 923~936 (SCI)

(4) Guantie Deng(#); Tao Qian(*), Rational Approximation of Functions in Hardy Spaces, Complex Analysis and Operator Theory, 2016, 10(5): 903~920 (期刊论文)

(5) 邓冠铁(#); 张艳慧, 次调和分析, 科学出版社， 166000, 2015.6.1 (学术专著)

(6) Guantie Deng, Une condition necessaire et suffisanté pour la quasi-analyticité de Mandelbrojt sur une demi-droite,C. R. Acad. Sci. Paris, 1988, 136(1): 769~772 (SCI)

(7) Guantie Deng, Theoreme d'existence et d'unicité pour les fonctions meromorphes dans un demi-plan, Bulletin des Sciences Mathematiques, 1989, 113(2): 443~462 (SCI)

(8) Yanhui Zhang(#); Kit Ian Kou; Guantie Deng, Integral representation and asymptotic behavior of harmonic functions in half space,, Journal of Differential Equations, 2014, 257: 2753~2764 (SCI)

(9) Guantie Deng, On weighted polynomial approximation with gaps, Nagoya Mathematical Journal, 2005, 178: 55~61 (SCI)

(10) Guantie Deng, On Watson's Problem and its Application, Bulletin des Sciences Mathematiques, 1985, 2: 3~12 (SCI)

其它论文和论著

(1) Guantie Deng, Integral Representations of Harmonic Functions in Half Spaces, Bulletin des Sciences Mathematiques,2007, 131: 53~59 (SCI)

(2) Guantie Deng, Incompleteness and minimality of complex exponential system, Science in China Series A-Mathematics,2007.10, 50(10): 1467~1476 (SCI)

(3) Pei Dang(#); Guantie Deng; Tao Qian, A Tighter UncertaintyPrinciple for Linear Canonical Transform in Terms of Phase Derivative, IEEE Transactions on signal Processing, 2013, 61(21): 5153~5164 (EI)

(4) Haichou Li; Guantie Deng(*); Tao Qian, Hardy space decomposition of L-p on the unit circle: 0(5) 张艳慧; 邓冠铁, 位势分析, 科学出版社, 220000, 2017 (学术专著)

(6) Yanhui Zhang; KitIan Kou; Guantie Deng; Tao Qian, The generalized Matsaev theorem on growth of subharmonic functions admitting a lower bound in R-n, Complex variables and elliptic equations , 2017, 62(5): 642~653 (SCI)

(7) Guantie Deng, Weighted exponential polynomial approximation, Science in China Series A-Mathematics, 2003, 46(2): 280~287 (SCI)

(8) Guantie Deng, Incompleteness and Closure of a Linear Span of Exponential System in a Weight Banach Space, Journal of Approximation Theory, 2003, 125: 1~9 (SCI)

(9) Guantie Deng, Uniqueness of some holomorphicFunctions, Chin.Ann.of Math., 1986, 7B(3): 330~338 (SCI)

(10) Zhiqiang Gao; Guantie Deng, The Generalized Bernstein Problem On Weighted Lacunary polynomial Approximation,Journal of Approximation Theorey, 2005, 136: 108~114 (SCI)

(11) Zhiqiang Gao; Guantie Deng, Muntz-type theorem onthe segments emerging from the origin, Journal of Approximation Theorey, 2008, 151: 181~185 (SCI)

(12) Lei Qiao(*); Guantie Deng, A THEOREM OF PHRAGMEN-LINDELOF TYPE FOR SUBFUNCTIONS IN A CONE , Glasgow Mathematical Journal, 2011, 53: 599~610 (SCI)

(13) Lei Qiao(*); Guantie Deng, Integral representation for the solution of the stationary Schrodinger equation in a cone , Mathematische Nachrichten, 2012, 285(16): 2029~2038 (SCI)

(14) Lei Qiao(*); Guantie Deng, Growth properties of modified alpha-potentials in the upper-half space , Filomat, 2013,27(4): 703~712 (SCI)

(15) Lei Qiao(*); Guantie Deng, Growth of certain harmonic functions in an n-dimensional cone , Frontiers of Mathematics in China, 2013, 8(4): 891~905 (SCI)

(16) Yanhui Zhang(*); Guantie Deng; KouKit Ian, ON THE LOWER BOUND FOR A CLASS OF HARMONIC FUNCTIONS IN THE HALF SPACE ,Acta Mathematica Scientia, 2012, 32(4): 1487~1494 (SCI)

(17) Yanhui Zhang(*); Kou, Kit Ian; Guantie Deng; Qian, Tao, The generalized Matsaev theorem on growth of subharmonic functions admitting a lower bound in R-n, Complex Variables and Elliptic Equations, 2017, 62(5): 642~653 (SCI)

(18) Pinhong Long(*); Zhiqiang Gao; Guantie Deng, Criteria of Wiener Type for Minimally Thin Sets and Rarefied Sets Associated with the Stationary Schrodinger Operator in a Cone , Abstract and Applied Analysis, 2012, 2012(1152) (SCI)

(19) Guoshuang Pan(*); Lei Qiao; Guantie Deng, Harmonic Functions in Upper Half Space , BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2012, 19(4): 675~681 (SCI)

(20) Huo Tang; Guantie Deng, Subordination and superordination preserving properties for a family of integral operators involving the Noor integral operator , Journal of the Egyptian Mathematical Society, 2014, 22(3): 352~361 (SCI) (期刊论文)

(21) Qiyu Jin(*); Guantie Deng; Daochun Sun, Julia lines of general random dirichlet series , Czechoslovak Mathematical Journal, 2012, 62(4): 919~936 (SCI)

(22) Huo Tang; Guantie Deng; Shuhai Li, Certain subclasses of p-valently analytic functions involving a generalized fractional differintegral operator , Journal of the Egyptian Mathematical Society, 2014, 22(1): 36~44 (SCI)

(23) Juhong Ning; Guantie Deng; Caifeng Yi, Incompleteness and closure of the multiplicity system {t(k)e(lambda)j(t)} in the weighted Banach space , Journal of Mathematical Analysis and Applications, 2008, 341(2): 1007~1017 (SCI)

(24) Lei Qiao; Baiyun Su; Guantie Deng, GROWTH PROPERTIES FOR THE SOLUTIONS OF THE STATIONARY SCHRODINGER EQUATION IN A CONE , Taiwanese Journal of Mathematics, 2012, 16(5): 1733~1748 (SCI)

(25) Yanhui Zhang; Guantie Deng, Integral Representation and Asymptotic Property of Analytic Functions with Order Less than Two in the Half-plane, Complex Variables theory and Application, 2005, 50(4): 283~297 (期刊论文)

(26) Huaping Huang(*); Guantie Deng; Radenovic, Stojan; Zhanmei Chen, Fixed point results for admissible mappings with application to integral equations , JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2016, 9(12): 6260~6273 (期刊论文)

(27) Pinhong Long(#); Guantie Deng(*), Some properties for subfunction associated withthe stationary Schr?dinger operator in a cone, Journal of Inequalities and Applications, 2012, 2012(2012) (SCI) (期刊论文)

(28) Yanhui Zhang; Guantie Deng; Kit Ian Kou, Asymptotic behavior of fractional Lpplacians in the half-space ,Application Mathematics and Computation, 2015, 254: 125~132 (SCI) (期刊论文)

(29) Guoshuang Pan(*); Lei Qiao; Guantie Deng, A lower estimate of harmonic functions , Bulletin of the Iranian Mathematical Society, 2014, 40(1): 1~7 (SCI) (期刊论文)

(30) Zhihong Wen(*); Guantie Deng; Cuiqiao Wang; Feifei Qu, Decomposition of L-p (partial derivative D-a) Space and Boundary Value of Holomorphic Functions , CHINESE ANNALS OF MATHEMATICS SERIES B, 2017, 38(5): 1093~1110 (SCI) (期刊论文)

(31) Lei Qiao(*); Guantie Deng, INTEGRAL REPRESENTATIONS AND GROWTH PROPERTIES FOR A CLASS OF SUPERFUNCTIONS IN A CONE ,Taiwanese Journal of Mathematics, 2011, 15(5): 2213~2233 (SCI) (期刊论文)

(32) Huo Tang(*); Guantie Deng; Shuhai Li; Aouf, M. K., Inclusion results for certain subclasses of spiral-like multivalent functions involving a generalized fractional differintegral operator , Integral Transforms and Special Functions, 2013, 24(11): 873~883(SCI)(期刊论文)

(33) Zhiqiang Gao; Guantie Deng, On weighted approximation by lacunary polynomials on the rays from the origin, Studia Scientiarum Mathematicrum Hungarica, 2008, 45(2): 197~205 (SCI) (期刊论文)

(34) Lei Qiao; Guantie Deng(*), Growth estimates for modified Green potentials in the upper-half space , Bulletin des Sciences Mathematiques, 2011, 135(3): 279~290 (SCI) (期刊论文)

(35) Huaping Huang(#)(*); Dolicanin-Dekic, Diana; Guantie Deng, On some recent fixed point results for (psi, phi)-contractive mappings in ordered partial b-metric spaces , Journal of Nonlinear Sciences and Applications, 2016, 9(7): 4990~4999 (SCI) (期刊论文)

(36) Guantie Deng, Completeness of complex exponential system, Chinese Journal of Contemporary Mathematics, 2005, 26(3): 313~318 (期刊论文)

(37) Zhiqiang Gao; Guantie Deng, On completeness and minimality of random exponential system in a weighted Banach space of functions continuous on the real line , Chinese Annals of Mathematics Series B, 2006, 27(3): 303~310 (SCI) (期刊论文)

(38) Huo Tang(*); Guantie Deng; Shuhai Li, On a certain new subclass of meromorphic close-to-convex functions , Journal of Inequalities and Applications, 2013, 2013(164): 1~6 (SCI) (期刊论文)

(39) Huo Tang(*); Aouf, M. K.; Guantie Deng; Shuhai Li, Differential Subordination Results for Analytic Functions in the Upper Half-Plane , Abstract and Applied Analysis, 2014, 565727(1): 1~6(SCI) (期刊论文)

(40) Huo Tang(#)(*); Guantie Deng; Sokol, Janusz; Shuhai Li, Inclusion and Argument Properties for the Srivastava-Khairnar-More Operator , Filomat, 2014, 28(8): 1603~1618 (SCI) (期刊论文)

(41) Huo Tang(*); Shuhai Li; Guantie Deng, MAJORIZATION PROPERTIES FOR A NEW SUBCLASS OF theta-SPIRAL FUNCTIONS OF ORDER gamma , Mathematica Slovaca, 2014, 64(1): 39~50 (SCI) (期刊论文)

(42) Huo Tang; Guantie Deng, Coefficient estimates for new subclasses of analytic functions with respect to other points, Tamkang Journal of Mathematics, 2013, 44(2): 141~148 (SCI) (期刊论文)

(43) Huo Tang(*); Guantie Deng; Shuhai Li, Coefficient estimates for new subclasses of Ma-Minda bi-univalent functions ,Journal of Inequalities and Applications, 2013, 2013(317): 1~10 (SCI) (期刊论文)

(44) Guantie Deng, Gap Theorems for entire Function, Kodai Mathmatical Journal, 1994, 17(1): 125~132 (期刊论文)

(45) Qiao, Lei(*); Deng, Guan-Tie, Growth Property and Integral Representation of Harmonic Functions in a Cone ,Bulletin of the Malaysian Mathematical Sciences Society, 2013, 36(2): 511~523 (SCI)(期刊论文)

(46) Lei Qiao(*); Guantie Deng, Growth properties of modified \$\alpha\$-potentials in the upper-half space, Filomat,2013, 27(4): 703~712 (SCI) (期刊论文)

(47) Guantie Deng, A generalization of Malliavin’s uniqueness theorem, Kodai Mathematical Journal , vol.23 (2000).p.320-325., 2000, 23: 320~325 (期刊论文)

(48) Guantie Deng, Hausdorff Dimension of a Fractal interpolation Function, Colloquium Mathematicum, 2004, 99(2): 275~281 (期刊论文)

(49) Guantie Deng, A note on the interpolation of entire functions, Southest Asian Bulletin of Mathematics, 2002, 26(3): 407~412 (期刊论文)

(50) Pinhong Long(#); Zhiqiang Gao; Guantie Deng(*), Criteria of Wiener type for minimally thin sets and rarefied sets associated with the stationary Schr?dinger operatorin a cone, Abstract and applied analysis, 2012, 2012(2012) (SCI) (期刊论文)

(51) Qiao, Lei; Deng, Guantie, Asymptotic Behavior for a Class of Modified alpha-Potentials in a Half Space , Journal of Inequalities and Applications, 2010, 2010(2010): 1-14 (SCI) (期刊论文)

(52) Jin Tu; Guantie Deng, Growth of solutions of certain higher order linear differential equations , Complex Variables and Elliptic Equations, 2008, 53(7): 623~631 (期刊论文)

(53) Zhiqiang Gao; Guantie Deng, On weighted approximation by lacunary polynomials on the rays emerging from the origin , Studia Scientiarum Mathematicarum Hungarica, 2008.6, 45(2): 197~205 (SCI) (期刊论文)

(54) Juhhong Ning; Guantie Deng, Completeness of the system {z(lambda n)} in L-2[B, alpha(0)] , Acta Mathematica Sinica-English Series, 2008, 24(12): 2101~2110 (SCI) (期刊论文)

(55) 邓冠铁, 复指数系的不完备性和最小性, 中国科学 A辑：数学, 2007.12.1, 37(7): 769~778 (期刊论文)

(56) 邓冠铁, 加权指数多项式逼近 , 中国科学A辑:数学, 2003, 33(3): 257~262 (期刊论文)

(57) 邓冠铁, 复指数系的完备性 , 数学年刊a辑, 2005, 26(4): 527~542 (期刊论文)

(58) 邓冠铁, 指数多项式在半带形中闭包, 数学物理学报, 2007.10.21, 27A(3): 414~419 (期刊论文)

(59) 邓冠铁, 半平面中有限阶解析函数的因子分解 , 数学学报, 2007, 50(01): 215~220 (期刊论文)

(60) 邓冠铁, 半平面中解析函数的积分表示, 数学学报, 2005.10.21, 48(3): 489~492 (期刊论文)

(61) 邓冠铁, 半平面中级小于2的解析函数的分解 , 数学物理学报, 2007, 27A(03): 414~419 (期刊论文)

(62) 乔蕾; 邓冠铁, 半空间中一类调和函数的例外集 , 数学年刊A辑(中文版), 2012.12.15, (06): 671~678 (期刊论文)

(63) 乔蕾; 邓冠铁, 锥中调和函数的积分表示 , 中国科学:数学, 2011, (06): 535~546 (期刊论文)

(64) 张艳慧; 邓冠铁, 半空间中一类次调和函数的增长性质 , Acta Mathematicae Applicatae Sinica-English Series, 2008.冬季,51(02): 319~326 (期刊论文)

(65) 乔蕾; 邓冠铁, 锥中调和函数的下界及其应用 , 中国科学:数学, 2014, (06): 671~684 (期刊论文)

(66) 乔蕾; 邓冠铁; 潘国双, 上半空间中修改的Poisson积分和Green位势的例外集, 中国科学:数学, 2010.8.15, 40(08): 787-800 (期刊论文)

(67) 乔蕾; 邓冠铁, 半空间中一类调和函数的例外集 , 数学年刊A辑(中文版), 2012, (06): 671~678 (期刊论文)

(68) 乔蕾; 邓冠铁, 广义带形区域中的Dirichlet问题, 中国科学:数学, 2013.7.10, 43(8): 781~792 (期刊论文)

(69) 柯思宇; 高志强; 邓冠铁, 随机指数系的完备性和极小性, 数学年刊A辑(中文版), 2010.8.8, 31A(04): 385-394 (期刊论文)

(70) 乔蕾; 邓冠铁, 锥内特定调和函数的渐近状态 , 数学学报, 2013.11.15, (06): 971~980 (期刊论文)

(71) 乔蕾; 邓冠铁, 锥中上调和函数的Riesz分解定理及其应用 , 中国科学:数学, 2012, (08): 765~776 (期刊论文)

(72) 乔蕾; 邓冠铁, 无穷远点处与Schr?dinger算子相关的极细集 , 中国科学:数学, 2014.12.20, (12): 1247~1256 (期刊论文)

(73) 乔蕾; 邓冠铁, 锥中一类调和函数的增长估计 , Acta Mathematicae Applicatae Sinica-English Series, 2011, (06): 1021~1028 (期刊论文)

(74) 邓冠铁; 李真, 给定零点的指数型整函数Ⅱ , 数学年刊A辑(中文版), 2011, (04): 423~434 (期刊论文)

(75) 邓冠铁, 指数多项式在半带形中的闭包 , 数学物理学报, 2007, 27A(03): 414~419 (期刊论文)

(76) 邓冠铁(*), 半平面中解析函数的积分表示 , 数学学报, 2005, 48(3): 489~492 (期刊论文)

(77) 邓冠铁, 半平面中解析函数的零点 , 数学物理学报, 2006, 26A(01): 45~48 (期刊论文)

(78) 邓冠铁(*), 复指数Dirichlet级数表示的整函数 , 数学物理学报, 2003, (06): 735~738 (期刊论文)

(79) 邓冠铁, 分形插值函数图像的Hausdorff维数, 数学学报, 1999, 42(1): 35~40 (期刊论文)

(80) 邓冠铁, 复指数级数表示的整函数, 数学物理学报, 2003, 23A(6): 735~738 (期刊论文)

(81) Guantie Deng, Incompletenessof Complex Exponential System in Banach Space, Northeast Mathematical Journal, 2004,20(3): 303~308 (期刊论文)

(82) 邓冠铁, Dimension of the Fractal Curve in Plane andIts Derivative of the Functional order, Northeast Mathematical Journal, 1995, 11(2): 1~8 (期刊论文)

(83) Guantie Deng, Representation Formulas for Analytic Function Non-exponential in a half-plane, Northeast Mathematical Journal, 1995, 11(2): 108~112 (期刊论文)

(84) Guantie Deng, Bouligand Dimension of Fractal Curve of Almost Periodic Series, Northest Mathematical Journal, 1998,14(1): 57~60 (期刊论文)

(85) 孔荫莹; 邓冠铁, Dirichlet级数的Dirichlet-Hadamard乘积 , 数学年刊A辑(中文版), 2014, 35A(2): 145~152 (期刊论文)

(86) 邓冠铁; 王翠巧, Lipshitz带形区域上的Hardy空间, 江西师范大学学报(自然科学版), 2017, 41(2): 175~179 (期刊论文)

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