000			02398nam a22002177a 4500
003			OSt
005			20241025120133.0
008			220607b |||||||| |||| 00| 0 eng d
020			_a9780486689234
040			_cDonation by CAM (Prof. A S Vasudeva Murthy) _aICTS-TIFR
050			_aQA320
100			_aGeorgi E.Shilov
245			_a Elementary functional analysis
260			_aNew York: _bDover Publication, _c[c1974]
300			_a334 p.
490			_a Graduate Texts in Mathematics _vVol. 253
505			_aChapter 1. Basic Structured of Mathematical Analysis Chapter 2. Differential Equation Chapter 3. Space Curves Chapter 4. Orthogonal Expansions Chapter 5. The Fourier Transform
520			_aIn this introductory work on mathematical analysis, the noted mathematician Georgi E. Shilov begins with an extensive and important chapter on the basic structures of mathematical analysis: linear spaces, metric spaces, normed linear spaces, Hilbert spaces, and normed algebras. The standard models for all these spaces are sets of functions (hence the term "functional analysis"), rather than sets of points in a finite-dimensional space.the basic theorems on existence and uniqueness of solutions of ordinary differential equations for functions taking values in a Banach space. The solution of the linear equation with constant (operator) coefficients is written in general form in terms of the exponential of the operator. This leads, in the finite-dimensional case, to explicit formulas not only for the solutions of first-order equations, but also to the solutions of higher-order equations and systems of equations. The third chapter presents a theory of curvature for curve in a multidimensional space. The final two chapters essentially comprise an introduction to Fourier analysis. In the treatment of orthogonal expansions, a key role is played by Fourier series and the various kinds of convergence and summability for such series. The material on Fourier transforms, in addition to presenting the more familiar theory, also deals with problems in the complex domain, in particular with problems involving the Laplace transform.Designed for students at the upper-undergraduate or graduate level, the text includes a set of problems for each chapter, with hints and answers at the end of the book.---Summary provided by publisher
650			_aMathematics
942			_2lcc _cBK
999			_c3130 _d3130