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maojun1998

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[交流] 《线性偏微分算子分析》L.Hormander（四卷全）【已搜素，无置重】已有2人参与

作者： Lars Hormander
丛书名： Grundlehren Der Mathematischen Wissenschaften
出版社：世界图书出版公司
ISBN：9787
上架时间：2014-3-10
出版日期：2005 年6月
开本：24开
页码：1705
版次：1-1
所属分类：数学 > 计算数学 > 偏微分

目录
《线性偏微分算子分析第1卷第2版(英文影印版)》
introduction
chapterⅰ test functions
summary
1.1 a review of differential calculus
1.2 existence of test functions
1.3 convolution
1.4 cutoff functions and partitions of unity
notes
chapterⅱ definition and basic properties of distributions
summary
2.1 basic definitions
2.2 localization
2.3 distributions with compact support
notes
chapterⅲ differentiation and multiplication by functions
summary
3.1 definition and examples
3.2 homogeneous distributions
3.3 some fundamental solutions
3.4 evaluation of some integrals
notes
chapterⅳ convolution
summary
4.1 convolution with a smooth function
4.2 convolution of distributions
4.3 the theorem of supports
4.4 the role of fundamental solutions
4.5 basic lp estimates for convolutions
notes
chapterⅴ distributions in product spaces
summary
5.1 tensor products
5.2 the kernel theorem
notes
chapterⅵ composition with smooth maps
summary
6.1 definitions
6.2 some fundamental solutions
6.3 distributions on a manifold
6.4 the tangent and cotangent bundles
notes
chapterⅶ the fourier transformation
summary
7.1 the fourier transformation in and in
7.2 poissons summation formula and periodic distributions
7.3 the fourier-laplace transformation in
7.4 more general fourier-laplace transforms
7.5 the malgrange preparatio theorem
7.6 fourier transforms of gaussian functions
7.7 the method of stationary phase
7.8 oscillatory integrals
7.9 h(s)lp and holder estimates
notes
chapterⅷ spectral analysis of singularities
summary
8.1 the wave front set
8.2 a review of operations with distributions
8.3 the wave front set of solutions of partial differential equations
8.4 the wave front set with respect to
8.5 rules of computation for wfl
8.6 wfl for solutions of partial differential equations
8.7 microhyperbolicity
notes
chapterⅸ hyperfunctions
summary
……
exercises
answers and hints to all the exercises
bibliography
index
index of notation

《线性偏微分算子分析第2卷第2版(英文影印版)》
introduction
chapter 10. existence and approximation of solutions of
differential equations
summary
10.1. the spaces bp.k
10.2. fundamental solutions
10.3. the equation p(d) u =f when
10.4. comparison of differential operators
10.5. approximation of solutions of homogeneous differential equations
10.6. the equation p(d)u=f when f is in a local space
10.7. the equation p(d) u =f when
10.8. the geometrical meaning of the convexity conditions
notes
chapter 11. interior regularity of solutions of differential equations
summary
11.1. hypoeuiptic operators
11.2. partially hypoelliptic operators
11.3. continuation of differentiability
11.4. estimates for derivatives of high order
notes
.chapter 12. the cauchy and mixed problems
summary
12.1 the cauchy problem for the wave equation
12.2 the oscillatory cauchy problem for the wave equation
12.3 necessary conditions for existence and uniqueness of solutions to the cauchy problem
……
chapter 13 differential operators of constant strength
chapter 14 scattering theory
chapter 15 analytic function theory and differential equations
chapter 16 convolution equations
appendix a. some algebraic lemmas
bibliography
index
index of notation

《线性偏微分算子分析第3卷第2版(英文影印版)》
introduction
chapter xvii. second order elliptic operators
summary
17.1. interior regularity and local existence theorems
17.2. unique continuation theorems
17.3. the dirichlet problem
17.4. the hadamard parametrix construction
17.5. asymptotic properties of eigenvalues and eigenfunctions
notes
chapter xviii. pseudo-differential operators
summary
18.1. the basic calculus
18.2. conormal distributions
18.3. totally characteristic operators
18.4. gauss transforms revisited
18.5. the weyl calculus
18.6. estimates of pseudo-differential operators
notes
chapter xix. elliptic operators on a compact manifold without
boundary
.summary
19.1. abstract fredholm theory
19.2. the index of elliptic operators
19.3. the index theorem in rn
19.4. the lefschetz formula
19.5. miscellaneous remarks on ellipticity
notes
chapter xx. boundary problems for elliptic differential operators
summary
20.1. elliptic boundary problems
20.2. preliminaries on ordinary differential operators
20.3. the index for elliptic boundary problems
20.4. non-elliptic boundary problems
notes
chapter xxi. symplectic geometry
summary
21.1. the basic structure
21.2. submanifolds of a sympletic manifold
21.3. normal forms of functions
21.4. folds and glancing hypersurfaces
21.5. symplectic equivalence of quadratic forms
21.6. the lagrangian grassmannian
notes
chapter xxii. some classes of (micro-)hypoelliptic operators
summary
22.1. operators with pseudo-differential parametrix
22.2. generalized kolmogorov equations
22.3. melin\'s inequality
22.4. hypoellipticity with loss of one derivative
notes
chapter xxiii. the strictly hyperbolic cauchy problem
summary
23.1. first order operators
23.2. operators of higher order
23.3. necessary conditions for correctness of the cauchy
problem
23.4. hyperbolic operators of principal type
notes
chapter xxiv. the mixed dirichlet-cauchy problem for second order
operators
summary
24.1. energy estimates and existence theorems in the
hyperbolic case
24.2. singularities in the elliptic and hyperbolic regions
24.3. the generalized bicharacteristic flow
24.4. the diffractive case
24.5. the general propagation of singularities
24.6. operators microlocally of tricomi\'s type
24.7. operators depending on parameters
notes
appendix b. some spaces of distributions
b.1. distributions in irn and in an open manifold
b.2. distributions in a half space and in a manifold
with boundary
appendix c. some tools from differential geometry
c.1. the frobenius theorem and foliations
c.2. a singular differential equation
c.3. clean intersections and maps of constant rank
c.4. folds and involutions
c.5. geodesic normal coordinates
c.6. the morse lemma with parameters
notes
bibliography
index
index of notation

《线性偏微分算子分析第4卷第2版(英文影印版)》
introduction
chapter xxv. lagrangian distributions and fourier integral
operators
summary
25.1. lagrangian distributions
25.2. the calculus of fourier integral operators
25.3. special cases of the calculus， and l2 continuity
25.4. distributions associated with positive lagrangian ideals
25.5. fourier integral operators with complex phase
notes
chapter xxvi. pseudo-differential operators of principal type
summary
26.1. operators with real principal symbols
26.2. the complex involutive case
26.3. the symplectic case
26.4. solvability and condition (ψ)
26.5. geometrical aspects of condition (p)
26.6. the singularities in n11
26.7. degenerate cauchy-riemann operators
26.8. the nirenberg-treves estimate
. 26.9.the nrenberg-treves estimate
26.10.the singularites on one dimensional bicharacterstics
26.11.a semi-global existence theorem
chapter xxvii.subelliptic operators
summary
27.1.defintions and main results
27.2.the taylor expansion of the symbol
27.3.subelliptic operators satsfying(p)
27.4.local properties of the symbol
chapter xxviiii.uniqueess for the cauchy problem
chapter xxix.spectral asymptotics
chapter xxx.long range scattering theory
bibliography
index
index of notation
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