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Kuchment P. — Floquet theory for partial defferential equations
Kuchment P. — Floquet theory for partial defferential equations

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Название: Floquet theory for partial defferential equations

Автор: Kuchment P.


Chapter 1 contains some preliminary information on functional analysis, operator theory and complex analysis. The main results that will play the major role in the following chapters are concentrated in sections 1.7 and 1.8. They are rather technical, and I recommend to the reader who is interested mainly in differential equations to skip chapter 1 on the first reading. The statements of the main results of chapters 2-6 can be understood without referring to sections 1.7 and 1.8. The proofs, however, depend strongly on chapter 1. Chapter 2 provides the definitions and properties of transforms that play the role of the Fourier transform. Chapter 3 is devoted to the principal results of the Floquet theory for hypoelliptic equations. In chapter 4 it is shown how the Floquet theory is related to other properties of periodic equations (for instance, to spectral theory). Chapter 5 treats in more detail the case of evolution equations of hypoelliptic (in particular, parabolic) type. Writing this chapter, I found out that it was impossible to cover in one chapter even the case of time-periodic parabolic equations. I plan to give a more complete account of this topic in another publication. Chapter 6 contains a brief consideration of related problems: equations with deviating arguments, more general groups of periods, etc. Every chapter has a final section devoted to additional comments and references.

Язык: en

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 350

Добавлена в каталог: 15.04.2005

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Предметный указатель
AF-sheaf      63
Banach adjoint      24
Banach associated      24
Banach base      22
Banach fiber      21
Banach holomorphic      62
Banach of countable type      22
Banach of finite type      22
Banach space      22
Banach trivial      22
Banach vector bundle      22
Band function      152
BCAF-sheaf      64
Bloch solution      104
Bloch variety      152
Calkin algebra      11
Compactification directional      157
Complemented subbundle      23
Cospectrum      74
Cover trivializing      21
Covering condition      245
Dirac operator      141
Direct subbundle      23
Dirichlet system      245
dispersion relation      152
Domain pseudoconvex      68
Ellipticity      115 245
Entire function of finite order      33
Floquet exponent      104
Floquet multiplier      104
Floquet solution      103 104
Floquet variety      155
Function entire of finite order      33
Germ associated      58
Grassmanian      25
Green's formula      245 246
Heisenberg group      300
Ideal associated      56
Index of a family      29
Index of a Fredholm operator      6
Isomorphism of bundles      22
Lasker-Noether decomposition      56
Module $\mathfrak{B}$-coprimary      56
Morphism Fredholm      22
Morphism holomorphic      71
Morphism of a bundle      22
Nerve axon system      261
Normality condition      245
Operator $\mathfrak{B}$-Noether      57
Operator differential in modules      57
Operator differential in sheaves      57
Operator elliptic in Douglis-Nirenberg sense      115
Operator Fredholm      6
Operator hypoelliptic      116 117
Operator Noether      57
Operator of $\mathscr{S}_p$ class      15
Operator proper pseudodifferential      92
Operator semi-Fredholm      6
Operator transversally-elliptic      269
Operator Y-Noether      58
Order of a differential operator      57
Paley-Wiener space      285
Parametrix      92
Projection of a bundle      21
Reaction-diffusion system      260 261
Regularized determinant      17
Regularizer      10
s-numbers (singular values)      15
Section holomorphic      62
Set analytic      58
Set irreducible      58
Shatten-von Neumann class      15
Sheaf analytic      55
Sheaf analytic Frechet      63
Sheaf Banach coherent      64
Sheaf coherent      55
Sheaf locally finite generated      55
Sheaf of relations      55
Space $\mathscr{UF}$      5
Space of the type $(\beta)$      5
Spectrum      74
Stein manifold      54
Strongly damped wave equation      260
Trivializing maps      21
Weak uniqueness property      132
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