Differential Analysis

F.Y.M. Wan, Introduction to Calculus of Variations and Its Applications, Chapman & Hall, 1995

G. Whitham, “Linear and Nonlinear Waves”, John-Wiley and Sons, 1974.

J. Keener, “Principles of Applied Mathematics”, Addison-Wesley, 1988.

A. Benssousan, P-L Lions, G. Papanicolaou, “Asymptotic Analysis for Periodic Structures”,  North-Holland Publishing Co,  1978. 

V. Jikov, S. Kozlov, O. Oleinik, “Homogenization of differential operators and integral functions”,  Springer, 1994.

J. Xin, “An Introduction to Fronts in Random Media”, Surveys and Tutorials in Applied Math Sciences, No. 5, Springer, 2009.

Integral Equations

 Masujima, M. Applied Mathematical Methods of Theoretical Physics – Integral Equations and Calculus of Variations. Weinheim, Germany: Wiley-VCH, 2005. ISBN: 3527405348.

Dynamical System

《微分方程、动力系统与混沌导论》Morris W.Hirsch，Stephen Smale，Robert Devaney

《Differential Equations，Dynamical Systems and Linear Algebra》

《微分动力系统原理》张筑生

Harmonic Analysis

An Introduction to Harmonic Analysis,Third Edition Yitzhak Katznelson：

A Course in Abstract Harmonic Analysis by Folland：

Abstract Harmonic Analysis by Ross Hewitt：

Harmonic Analysis by Elias M. Stein：

齐民友《广义函数与数学物理方程》高等教育出版社

王竹溪,郭敦仁 “特殊函数概论” 

调和分析中的不确定性原理

1，Heisenberg不等式，Amreyn-Berthier定理。

2，Nazarov不等式，Turan-Nazarov引理。

3，Fourier级数的符号定理，Mikheev定理。

4，复方法，作为不确定性原理表现的解析函数的唯一边界定理。

5，Berling-Malyaven定理。

6，间隔幂级数的Fabry定理，圆盘上广义函数的不确定性原理。

7，Newton与Risze位势的不确定性原理。

8，Laplace方程的Cauchy问题，Bers-Lavrentyev猜想。

9，Wolf-Burgeyn反例。

1，V.Havin、B.Joericke，The Uncertainty Principle in Harmonic Analysis，Springer-Verlag，1994。

2，V.P.Havin、N.K.Nikolski，Lecture Notes In Math，Vol 1573，Springer-Verlag，1994。

3，V.P.Havin、N.K.Nikolski，Lecture Notes In Math，Vol 1574，Springer-Verlag，1994。

4，L.V.Kantorovich、G.P.Akilov，泛函分析，科学出版社，1977。

Microlocal Analysis & Wavelet, Filter Bank & Wave Propagation

Strang, and Nguyen. Wavelets and Filter Banks. Wellesley-Cambridge Press, 1997.

Differential Analysis

F.Y.M. Wan, Introduction to Calculus of Variations and Its Applications, Chapman & Hall, 1995

G. Whitham, “Linear and Nonlinear Waves”, John-Wiley and Sons, 1974.

J. Keener, “Principles of Applied Mathematics”, Addison-Wesley, 1988.

A. Benssousan, P-L Lions, G. Papanicolaou, “Asymptotic Analysis for Periodic Structures”, North-Holland Publishing Co, 1978.

V. Jikov, S. Kozlov, O. Oleinik, “Homogenization of differential operators and integral functions”, Springer, 1994.

J. Xin, “An Introduction to Fronts in Random Media”, Surveys and Tutorials in Applied Math Sciences, No. 5, Springer, 2009.

Integral Equations

 Masujima, M. Applied Mathematical Methods of Theoretical Physics – Integral Equations and Calculus of Variations. Weinheim, Germany: Wiley-VCH, 2005. ISBN: 3527405348.

Dynamical System

Introduction to differential equations, dynamical systems and chaos Morris W.Hirsch , Stephen Smale , Robert Devaney

《 Differential Equations , Dynamical Systems and Linear Algebra 》

The principle of differential dynamic system build

Harmonic Analysis

An Introduction to Harmonic Analysis,Third Edition Yitzhak Katznelson :

A Course in Abstract Harmonic Analysis by Folland :

Abstract Harmonic Analysis by Ross Hewitt :

Harmonic Analysis by Elias M. Stein :

Aligned friends of the generalized functions and equations of mathematical physics higher education press

Wang Zhuxi , Guo d r ” Introduction to special functions”

Harmonic analysis of the uncertainty principle

1 , Heisenberg Inequalities, Amreyn-Berthier Theorem.

2 , Nazarov Inequalities, Turan-Nazarov Lemma.

3 , Fourier Series symbol theorem Mikheev Theorem.

4 , And, as the only border uncertainty principle of analytic functions theorem.

5 , Berling-Malyaven Theorem.

6 Interval power series Fabry Theorem of generalized function on the disk of the uncertainty principle.

7 , Newton Risze Potential of the uncertainty principle.

8 , Laplace Equation Cauchy Problem Bers-Lavrentyev Guess.

9 , Wolf-Burgeyn Counter examples.

1 , V.Havin 、 B.Joericke , The Uncertainty Principle in Harmonic Analysis , Springer-Verlag , 1994 。

2 , V.P.Havin 、 N.K.Nikolski , Lecture Notes In Math , Vol 1573 , Springer-Verlag , 1994 。

3 , V.P.Havin 、 N.K.Nikolski , Lecture Notes In Math , Vol 1574 , Springer-Verlag , 1994 。

4 , L.V.Kantorovich 、 G.P.Akilov , Functional analysis, science press, 1977 。

Microlocal Analysis & Wavelet, Filter Bank & Wave Propagation

Strang, and Nguyen. Wavelets and Filter Banks. Wellesley-Cambridge Press, 1997.