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Operator approach in linear problems of hydrodynamics:volume 1:self-adjoint prob

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Operator approach in linear problems of hydrodynamics:volume 1:self-adjoint problems for an ideal fluid液体动力学线性问题的算子方法 第1卷:理想流体的自伴问题水利图书+u QuL{7P(|2s!g-W|

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作  者: Nikolay D. Kopachevskii 等著水利图书,SB+RN s$Z,wj

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出 版 社:

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&{%]Tx#Iazy'KBX0出版时间: 2001-10-1水利图书(\7J} d4b

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字  数:

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版  次: 1

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页  数: 384

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印刷时间: 2001-10-1

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\&C0h*}@j0开  本: 16开

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印  次: 1水利图书)NuJ{r

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I S B N : 9783764354060水利图书A]Ml?%@'^g

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所属分类: 图书 >> 进口原版书 >> 科学与技术 Science & Techology

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内容简介水利图书9]%M)GwVN,M

wcq+D T8pW[.v4{)}0This is the first volume of a set of two devoted to the operator approach to linear problems in hydrodynamics. It presents functional analytical methods applied to the study of small movements and normal oscillations of hydromechanical systems having cavities filled with either ideal or viscous fluids. The work is a sequel to and at the same time substantially extends the volume "Operator Methods in Linear Hydrodynamics: Evolution and Spectral Problems" by N.D. Kopachevsky, S.G. Krein and Ngo Zuy Kan, published in 1989 by Nauka in Moscow. It includes several new problems on the oscillations of partially dissipative hydrosystems and the oscillations of visco-elastic or relaxing fluids. The work relies on the authors' and their students' works of the last 30-40 years. The readers are not supposed to be familiar with the methods of functional analysis. In the first part of the present volume, the main facts of linear operator theory relevant to linearized problems of hydrodynamics are summarized, including elements of the theories of distributions, self-adjoint operators in Hilbert spaces and in spaces with an indefinite metric, evolution equations and asymptotic methods for their solutions, the spectral theory of operator pencils. The book is particularly useful for researchers, engineers and students in fluid mechanics and mathematics interested in operator theoretical methods for the analysis of hydrodynamical problems.水利图书['@3y^&C2y-r

Y9m$T Gt L5I5R0目录水利图书B U@-n9Z)G

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Volume I水利图书FV%oB ? s"|

j*J6W9O(Kvq0Preface水利图书 {~1Y%yKC

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Table of Contents

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b sx'FL@!yC0 Volume I水利图书)G2jO t/}hp

-a-?_ ix}0 Volume II水利图书%}S(yj$xC'C

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Introduction

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Part 1 Mathematical Foundations of Linear Hydrodynamics . .

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N#{"J ya1fs0Chapter 1: Operators on Hilbert Spaces水利图书$d,XzlHNs

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 1.1 General Facts水利图书7M%c C1G sD5xJ

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  1.1.1 The Concept of a Hilbert Space

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4sp;G H#YqU0  1.1.2 The Space L2

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  1.1.3 Orthogonality. Projection onto a Subspace水利图书3xr!yx'R mS*\e

ap+G5SE/`0  1.1.4 Equivalent Norms水利图书iK1]*`g W0MXB

h9Dx oDbd0  1.1.5 Linear Functionals. Riesz Theorem水利图书AS)^8{)xDC

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  1.1.6 Embeddings of Spaces. Riesz Theorem for Equipments水利图书1Jz{.e*@B"iK Y

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  1.1.7 Orthonormal Systems and Bases

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;i nB'Z x6K$o0  1.1.8 Bounded Linear Operators水利图书K4G DI0~#v4o@

an PC'H0FX&|0  1.1.9 Adjoint Operators

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  1.1.10 Self-Adjoint Operators水利图书%VvM+n)R&c$jFL

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  1.1.11 Self-Adjoint Compact Operators水利图书+d&tW.i%r5_S:^I6L

8L8jI0m}ESu0  1.1.12 Compact operators, s-numbers

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+|(fFNu#zy01.1.13 Riesz Bases and p-Bases水利图书 ap_0} tw,B

B~8u#GW%R01.1.14 Direct Sum of Subspaces. Invariant Subspaces水利图书(NB4I*b0?m

4zBK f0c01.1.15 Eigen- and Associated (Root) Elements. Root Subspaces .

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1.1.16 Unbounded Linear Operators水利图书9^'bht tM*h

R1L0lW1C U$CB01.1.17 Resolvent and Spectrum of a Linear Operator

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1.1.18 Classification of Points in the Spectrum of a Linear Operator

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1.1.19 Spectrum of a Self-Adjoint Operator. Weyl Theorem . . .水利图书/c8K6K2q2T,j:K.{

a)nMmG/A"kE'Do01.1.20 Riesz Projections水利图书C i"Z\G`9b!vx

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1.1.21 Symmetric and Self-Adjoint Operators

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1.1.22 Spectral Decomposition of Self-Adjoint Operators. Functions of Operators水利图书)t h j)Z(~*v

6J!`9rh-~am01.1.23 Spaces with Degenerate Scalar Products. Seminorms . . .

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1.1.24 Equivalent Corrections of Seminorms

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 1.2 Sobolev Spaces水利图书V1L+J(J`,d.gu

Y-|yv|klp&{4X)p6@01.2.1 Finite Functions

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1.2.2 Generalized Derivatives

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"j&l,U!bEx01.2.3 The Definition of Sobolev Spaces

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e2V4}.cat1c$R01.2.4 The Space L2. Regions of the First Type .

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1o^] \F cPWL01.2.5 The Subspace H01

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(X)J G*|/y G)O2jM2a01.2.6 Embedding H1 into L2 Regions of the Second Type水利图书9?'^nl8e8g-b*`

w9Rr;Zt01.2.7 The Trace Operator. Regions of the Third Type水利图书6Z(xN#Bw

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 1.3 Spaces With Indefinite Metrics水利图书~*IW0m]4`1I&T i8[

%gm-r1Vz n01.3.1 J-Spaces水利图书urM:A%NB&N9B3Q

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1.3.2 Uniformly Definite Subspaces水利图书,}F6h)U-avl;]

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1.3.3 J-Orthonormal Systems and Bases

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1.3.4 Linear Operators on J-Spaces水利图书+|nqxe qH3C#No

{`k M(l_~01.3.5 Invariant Subspaces of J-Self-Adjoint Operators水利图书`C8[1{%j ys0V

%D%t4BO MCeR01.3.6 Pontryagin Spaces水利图书We9v}N

Z0vnFu9p3z01.3.7 On Completeness and Basicity for the System of Root Elements of a J-Self-Adjoint Operator水利图书:m1lRaY5M:M[:_(u

xSg }7Z] _0 1.4 Eigenvalue Problems

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5`+X6] f(R*O(M01.4.1 Operator B is the Identity Operator水利图书~b4D g W7FwB

x}m:E8` b!D!H#VXj0  1.4.2 Operator B is Positive Definite

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  1.4.3 Positivity Condition for a Matrix Operator

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D9~;h F[0  1.4.4 Simplifying Equations with an Alternating Operator

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;VZ$wZ6v ?0 Chapter 2:Fundamental Spaces and Operators of Linear Hydrodynamics水利图书.Kvz;p$ee/W0o@L

$G3e}iK$X `0Part 2: Motion of Bodies With Cavities Containing Ideal Fluids

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)yvjsd;M v+z)mk A0Chapter 3:Oscillations of a Heavy Ideal Fluid in Stationary and Nonstationay Contatiners水利图书'P[7Io7c`M

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