Mathematical analysis : a special course / [by] G. Ye. Shilov. Translated by J.D. Davis. English translation edited by D.A.R. Wallace.
Idioma: Inglés Lenguaje original: Ruso Series International series of monographs in pure and applied mathematics ; v. 77Editor: Oxford ; New York : Pergamon Press, [1965]Edición: [1st ed.]Descripción: xii, 485 p. : il. ; 23 cmTema(s): Mathematical analysisOtra clasificación: 26.00CONTENTS Foreword xi Chapter I. Sets [1] 1. Sets, Subsets, Inclusions [1] 2. Operations on Sets [2] 3. Equivalence of Sets [5] 4. Countable Sets [9] 5. Sets of the Power of the Continuum [13] 6. Sets of Higher Powers [19] Chapter. II. Metric Spaces [21] 1. Definition and Examples of Metric Spaces. Isometry [21] 2. Open Sets [26] 3. Convergent Sequences and Closed Sets [28] 4. Complete Spaces [35] 5. Theorem of the Fixed Point [43] 6. Completion of a Metric Space [48] 7. Continuous Functions and Compact Spaces [52] 8. Normed Linear Spaces [62] 9. Linear and Quadratic Functions on a Linear Space [72] Chapter III. The Calculus oF Variations [78] 1. Differentiable Functionals [79] 2. Extrema of Differentiable Functionals [88] 3. Functionals of the Type ∫ab f(x, y, y') dx; [93] 4. Functionals of the Type ∫ab f(x, y, y') dx (continued) [108] 5. Functionals with Several Unknown Functions [119] 6. Functionals with Several Independent Variables [127] 7. Functionals with Higher Derivatives [134] Chapter IV. Theory of the Integral [142] 1. Sets of Measure Zero and Measurable Functions [142] 2. The Class C+ [148] 3. Summable Functions [156] 4. Measure of Sets and Theory of Lebesgue Integration [165] 5. Generalisations [179] Chapter V. Geometry of Hilbert Space [189] 1. Basic Definitions and Examples [189] 2. Orthogonal Resolutions [197] 3. Linear Operators [212] 4. Integral Operators with Square-summable Kernels [227] 5. The Sturm-Liouville Problem [236] 6. Non-homogeneous Integral Equations with Symmetric Kernels [246] 7. Non-homogeneous Integral Equations with Arbitrary Kernels [250] 8. Applications to Potential Theory [261] 9. Integral Equations with Complex Parameters [267] Chapter VI. Differentiation and Integration [282] 1. Derivative of a Non-decreasing Function [283] 2. Functions of Bounded Variation [295] 3. Determination of a Function from its Derivative [302] 4. Functions of Several Variables [310] 5. The Stieltjes Integral [319] 6. The Stieltjes Integral (continued) [330] 7. Applications of the Stieltjes Integral in Analysis [341] 8. Differentiation of Functions of Sets [352] Chapter VII. The Fourier Transform [359] 1. On the Convergence of Fourier Series [359] 2. The Fourier Transform [380] 3. The Fourier Transform (continued) [392] 4. The Laplace Transform [403] 5. Quasi-analytic Classes of Functions [412] 6. The Fourier Transform in the Class L2(- ∞, ∞) [421] 7. The Fourier-Stieltjes Transform [436] 8. The Fourier Transform in the Case of Several Independent Variables [442] Supplement [456] 1. Further Remarks on Sets [456] 2. Theorems on Linear Functionals [460] Index [473] Other Titels in the Series [483]
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| 26 Se452 Calculus of one & several variables / | 26 Sh553 Funciones hiperbólicas / | 26 Sh556 Análisis matemático en el campo de funciones racionales / | 26 Sh556m Mathematical analysis : | 26 Si579 Advanced calculus : | 26 Si611 Análisis vectorial / | 26 Sm635 Subadditive and subquadratic set-valued functions / |
CONTENTS --
Foreword xi --
Chapter I. Sets [1] --
1. Sets, Subsets, Inclusions [1] --
2. Operations on Sets [2] --
3. Equivalence of Sets [5] --
4. Countable Sets [9] --
5. Sets of the Power of the Continuum [13] --
6. Sets of Higher Powers [19] --
Chapter. II. Metric Spaces [21] --
1. Definition and Examples of Metric Spaces. Isometry [21] --
2. Open Sets [26] --
3. Convergent Sequences and Closed Sets [28] --
4. Complete Spaces [35] --
5. Theorem of the Fixed Point [43] --
6. Completion of a Metric Space [48] --
7. Continuous Functions and Compact Spaces [52] --
8. Normed Linear Spaces [62] --
9. Linear and Quadratic Functions on a Linear Space [72] --
Chapter III. The Calculus oF Variations [78] --
1. Differentiable Functionals [79] --
2. Extrema of Differentiable Functionals [88] --
3. Functionals of the Type ∫ab f(x, y, y') dx; [93] --
4. Functionals of the Type ∫ab f(x, y, y') dx (continued) [108] --
5. Functionals with Several Unknown Functions [119] --
6. Functionals with Several Independent Variables [127] --
7. Functionals with Higher Derivatives [134] --
Chapter IV. Theory of the Integral [142] --
1. Sets of Measure Zero and Measurable Functions [142] --
2. The Class C+ [148] --
3. Summable Functions [156] --
4. Measure of Sets and Theory of Lebesgue Integration [165] --
5. Generalisations [179] --
Chapter V. Geometry of Hilbert Space [189] --
1. Basic Definitions and Examples [189] --
2. Orthogonal Resolutions [197] --
3. Linear Operators [212] --
4. Integral Operators with Square-summable Kernels [227] --
5. The Sturm-Liouville Problem [236] --
6. Non-homogeneous Integral Equations with Symmetric Kernels [246] --
7. Non-homogeneous Integral Equations with Arbitrary Kernels [250] --
8. Applications to Potential Theory [261] --
9. Integral Equations with Complex Parameters [267] --
Chapter VI. Differentiation and Integration [282] --
1. Derivative of a Non-decreasing Function [283] --
2. Functions of Bounded Variation [295] --
3. Determination of a Function from its Derivative [302] --
4. Functions of Several Variables [310] --
5. The Stieltjes Integral [319] --
6. The Stieltjes Integral (continued) [330] --
7. Applications of the Stieltjes Integral in Analysis [341] --
8. Differentiation of Functions of Sets [352] --
Chapter VII. The Fourier Transform [359] --
1. On the Convergence of Fourier Series [359] --
2. The Fourier Transform [380] --
3. The Fourier Transform (continued) [392] --
4. The Laplace Transform [403] --
5. Quasi-analytic Classes of Functions [412] --
6. The Fourier Transform in the Class L2(- ∞, ∞) [421] --
7. The Fourier-Stieltjes Transform [436] --
8. The Fourier Transform in the Case of Several Independent Variables [442] --
Supplement [456] --
1. Further Remarks on Sets [456] --
2. Theorems on Linear Functionals [460] --
Index [473] --
Other Titels in the Series [483] --
MR, 32 #2519
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