Fermilab Core Computing Division

Library Home |  Ask a Librarian library@fnal.gov |  Book Catalog |  Library Journals |  Requests |  SPIRES |  Fermilab Documents |

 Fermilab Library
SPIRES-BOOKS: FIND KEYWORD SEQUENCES,SERIES,SUMMABILITY *END*INIT* use /tmp/qspiwww.webspi1/16762.88 QRY 131.225.70.96 . find keyword sequences,series,summability ( in books using www

 Call number: SPRINGER-2003-9780817682323:ONLINE Show nearby items on shelf Title: Basic Real Analysis Author(s): Houshang H Sohrab Date: 2003 Size: 1 online resource (559 p.) Note: 10.1007/978-0-8176-8232-3 Contents: 1 Set Theory -- 1.1 Rings and Algebras of Sets -- 1.2 Relations and Functions -- 1.3 Basic Algebra, Counting, and Arithmetic -- 1.4 Infinite Direct Products, Axiom of Choice, and Cardinal Numbers -- 1.5 Problems -- 2 Sequences and Series of Real Numbers -- 2.1 Real Numbers -- 2.2 Sequences in ? -- 2.3 Infinite Series -- 2.4 Unordered Series and Summability -- 2.5 Problems -- 3 Limits of Functions -- 3.1 Bounded and Monotone Functions -- 3.2 Limits of Functions -- 3.3 Properties of Limits -- 3.4 One-sided Limits and Limits Involving Infinity -- 3.5 Indeterminate Forms, Equivalence, Landau’s Little “oh” and Big “Oh” -- 3.6 Problems -- 4 Topology of ? and Continuity -- 4.1 Compact and Connected Subsets of ? -- 4.2 The Cantor Set -- 4.3 Continuous Functions -- 4.4 One-sided Continuity, Discontinuity, and Monotonicity -- 4.5 Extreme Value and Intermediate Value Theorems -- 4.6 Uniform Continuity -- 4.7 Approximation by Step, Piecewise Linear, and Polynomial Functions -- 4.8 Problems -- 5 Metric Spaces -- 5.1 Metrics and Metric Spaces -- 5.2 Topology of a Metric Space -- 5.3 Limits, Cauchy Sequences, and Completeness -- 5.4 Continuity -- 5.5 Uniform Continuity and Continuous Extensions -- 5.6 Compact Metric Spaces -- 5.7 Connected Metric Spaces -- 5.8 Problems -- 6 The Derivative -- 6.1 Differentiability -- 6.2 Derivatives of Elementary Functions -- 6.3 The Differential Calculus -- 6.4 Mean Value Theorems -- 6.5 L’Hôpital’s Rule -- 6.6 Higher Derivatives and Taylor’s Formula -- 6.7 Convex Functions -- 6.8 Problems -- 7 The Riemann Integral -- 7.1 Tagged Partitions and Riemann Sums -- 7.2 Some Classes of Integrable Functions -- 7.3 Sets of Measure Zero and Lebesgue’s Integrability Criterion -- 7.4 Properties of the Riemann Integral -- 7.5 Fundamental Theorem of Calculus -- 7.6 Functions of Bounded Variation -- 7.7 Problems -- 8 Sequences and Series of Functions -- 8.1 Complex Numbers -- 8.2 Pointwise and Uniform Convergence -- 8.3 Uniform Convergence and Limit Theorems -- 8.4 Power Series -- 8.5 Elementary Transcendental Functions -- 8.6 Fourier Series -- 8.7 Problems -- 9 Normed and Function Spaces -- 9.1 Norms and Normed Spaces -- 9.2 Banach Spaces -- 9.3 Hilbert Spaces -- 9.4 Function Spaces -- 9.5 Problems -- 10 The Lebesgue Integral (F. Riesz’s Approach) -- 10.1 Improper Riemann Integrals -- 10.2 Step Functions and Their Integrals -- 10.3 Convergence Almost Everywhere -- 10.4 The Lebesgue Integral -- 10.5 Convergence Theorems -- 10.6 The Banach Space L1 -- 10.7 Problems -- 11 Lebesgue Measure -- 11.1 Measurable Functions -- 11.2 Measurable Sets and Lebesgue Measure -- 11.3 Measurability (Lebesgue’s Definition) -- 11.4 The Theorems of Egorov, Lusin, and Steinhaus -- 11.5 Regularity of Lebesgue Measure -- 11.6 Lebesgue’s Outer and Inner Measures -- 11.7 The Hilbert Spaces L2(E, % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXguY9 % gCGievaerbd9wDYLwzYbWexLMBbXgBcf2CPn2qVrwzqf2zLnharyav % P1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC % 0xbbL8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yq % aqpepae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabe % qaamaaeaqbaaGcbaWefv3ySLgznfgDOjdarCqr1ngBPrginfgDObcv % 39gaiyaacqWFfcVraaa!47BC! $$\mathbb{F}$$) -- 11.8 Problems -- 12 General Measure and Probability -- 12.1 Measures and Measure Spaces -- 12.2 Measurable Functions -- 12.3 Integration -- 12.4 Probability -- 12.5 Problems -- A Construction of Real Numbers -- References ISBN: 9780817682323 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Keywords: Mathematics , Mathematical analysis , Analysis (Mathematics) , Measure theory , Functions of real variables , Mathematical logic , Mathematics , Real Functions , Analysis , Measure and Integration , Mathematical Logic and Foundations Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE

 Call number: SPRINGER-1996-9789400902831:ONLINE Show nearby items on shelf Title: Trigonometric Fourier Series and Their Conjugates Author(s): Levan Zhizhiashvili Date: 1996 Size: 1 online resource (308 p.) Note: 10.1007/978-94-009-0283-1 Contents: Preface -- 1 Simple Trigonometric Series -- I. The Conjugation Operator and the Hilbert Transform -- II. Pointwise Convergence and Summability of Trigonometric Series -- III. Convergence and Summability of Trigonometric Fourier Series and Their Conjugates in the Spaces $$L^p \left( T \right),p \in \left] {0, + \infty } \right[$$ -- IV. Some Approximating Properties of Cesaro Means of the Series $$\sigma \left[ f \right]$$ and $$\bar \sigma \left[ f \right]$$ -- 2 Multiple Trigonometric Series -- I. Conjugate Functions and Hilbert Transforms of Functions of Several Variables -- II. Convergence and Summability at a Point or Almost Everywhere of Multiple Trigonometric Fourier Series and Their Conjugates -- III. Some Approximating Properties of n-Fold Cesaro Means of the Series $$\sigma _n \left[ f \right]$$ and $$\sigma _n \left[ {f,B} \right]$$ -- IV. Convergence and Summability of Multiple Trigonometric Fourier Series and Their Conjugates in the Spaces $$L^p \left( {T^n } \right),p \in \left] {0, + \infty } \right]$$ -- V. Summability of Series $$\sigma _2 \left[ f \right]$$ and $$\bar \sigma _2 \left[ {f,B} \right]$$ by a Method of the Marcinkiewicz Type ISBN: 9789400902831 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Series: Mathematics and Its Applications : 372 Keywords: Mathematics , Approximation theory , Fourier analysis , Integral transforms , Operational calculus , Functions of real variables , Sequences (Mathematics) , Mathematics , Fourier Analysis , Approximations and Expansions , Integral Transforms, Operational Calculus , Sequences, Series, Summability , Real Functions Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE