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MARC 21

Hausdorff Approximations
Tag	Description
020	$a9789400906730
082	$a514.3
099	$aOnline resource: Springer
100	$aSendov, Blagovest
245	$aHausdorff Approximations$h[EBook]$cby B. Sendov ; edited by Gerald Beer.
260	$aDordrecht$bSpringer Netherlands$c1990.
300	$a388 pages$bonline resource.
336	$atext
338	$aonline resource
440	$aMathematics and Its Applications, East European Series,$x0169-507X ;$v50
505	$a1 Elements of segment analysis -- § 1.1. Segment arithmetic -- § 1.2. Segment sequences -- § 1.3. Segment functions -- 2 Hausdorff distance -- § 2.1. Hausdorff distance between subsets of a metric space -- § 2.2. The metric space F? -- § 2.3. H-distancein A? and its properties -- § 2.4. Relationships between uniform distance and the Hausdorff distance -- § 2.5. The modulus of H-continuity -- § 2.6. The order of the modulus of H-continuity -- § 2.7. H-continuity on a subset -- § 2.8. H-distance with weight -- 3 Linear methods of approximation -- § 3.1. Convergence of sequences of positive operators -- § 3.2. The order of approximation of functions by positive linear operators -- § 3.3. Approximation of periodic functions by positive integral operators -- § 3.4. Approximation of functions by positive integral operators on a finite closed interval -- § 3.5. Approximation of functions by summation formulas on a finite closed interval -- § 3.6. Approximation of nonperiodic functions by integral operators on the entire real axis -- § 3.7. Convergence of derivatives of linear operators -- § 3.8. A-distance -- § 3.9. Approximation by partial sums of Fourier series -- 4 Best Hausdorff approximations -- § 4.1. Best approximation by algebraic and trigonometric polynomials -- § 4.2. Best approximation by rational functions -- § 4.3. Best approximation by spline functions -- § 4.4. Best approximation by piecewise monotone functions -- 5 Converse theorems -- § 5.1. Existence of a function with preassigned best approximations -- § 5.2. Converse theorems for the approximation by algebraic and trigonometric polynomials -- § 5.3. Converse theorems for approximation by spline functions -- § 5.4. Converse theorems for approximation by rational and partially monotone functions -- § 5.5. Converse theorems for approximation by positive linear operators -- 6 ?-Entropy, ?-capacity and widths -- § 6.1. ?-entropy and ?-capacity of the set F?M -- § 6.2. The number of (p,q)-corridors -- § 6.3. Labyrinths -- § 6.4. ?-entropy and ?-capacity of bounded sets of connected compact sets -- § 6.5. Widths -- 7 Approximation of curves and compact sets in the plane -- § 7.1. Approximation by polynomial curves -- § 7.2. Characterization of best approximation in terms of metric dimension -- § 7.3. Approximation by piecewise monotone curves -- § 7.4. Other methods for the approximation of curves in the plane -- 8 Numerical methods of best Hausdorff approximation -- § 8.1. One-sided Hausdorff distance -- § 8.2. Coincidence of polynomials of best approximation with respect to one- and two-sided Hausdorff distance -- § 8.3. Numerical methods for calculating the polynomial of best one-sided approximation -- References -- Author Index -- Notation Index.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
700	$aBeer, Gerald.$eeditor.
710	$aSpringerLink (Online service)
830	$aMathematics and Its Applications, East European Series,$v50
856	$uhttp://dx.doi.org/10.1007/978-94-009-0673-0