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Numerieke zaken uit Analyse
Numerieke zaken uit AnalyseDr. J.H.J. Almering e.a.Regula falsi
Linearisering, interpolatieformule van Lagrange, numerieke nulpuntsbepaling
Numerieke integratie
Foutenleer
Gewone differentiaalvergelijkingen (de methode van Heun)
Rijen en reeksen
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Harmonische Räume und ihre Potentialtheorie
Harmonische Räume und ihre PotentialtheorieHeinz BauerI. Harmonische Räume
II. Superharmonische Funktionen und Potentiale
III. Balayage-Theorie
IV. Dirichletsche Problem
V. Zerlengungs- und Fortsetzungssatz
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Potential Theory
Potential TheoryJohn Wermer2. Electrostatics
3. Poisson's Equation
4. Fundamental Solutions
5. Capacity
6. Energy
7. Existence of the Equilibrium Potential
8. Maximum Principle for Potentials
9. Uniqueness of the Equilibrium Potential
10. The Cone Condition
11. Singularities of Bounded Harmonic Functions
12. Green's Function
13. The Kelvin Transform
14. Perron's Method
15. Barriers
16. Kellogg's Theorem
17. The Riesz Decomposition Theorem
18. Applications of the Riesz Decomposition
19. Appendix
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The cos πλ Theorem
The cos πλ TheoremMatts R. Essén1. The Hellsten-Kjellberg-Norstad inequality
2. The cos πλ -theorem
3. A generalization of the Ahlfors-Heins theorem
4. The Paley conjecture
5. A cos πλ -problem an da differential inequality
6. A counterexample
7. Proof of theorem 5.2
8. Two consequences of a theorem of A. Baernstein
9. On two theorems of A. Baernstein
10. References
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Univalent Functions - Selected Topics
Univalent Functions - Selected TopicsGlenn Schober1. Functions with positive real part
2. Special classes: convex, starlike, real, typically real, close-to-convex, bounded boundary rotation
3. The Pólya-Schoenberg conjecture
4. Representation of continuous linear functionals
5. Faber polynomials
6. Extremal length and equicontinuity
7. Compact families ℱ(D,ℓ1,ℓ2,P,Q) of univalent functions normalized by two linear functionals
8. Properties of extreme points for some compact families ℱ(D...
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Theta Functions on Riemann Surfaces
Theta Functions on Riemann SurfacesJohn D. FayI. Riemann's theta function
II. The prime-form
III. Degenerate Riemann surfaces
IV. Cyclic unramified coverings
V. Ramified double coverings
VI. Bordered Riemann surfaces
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Analytic Capacity and Measure
Analytic Capacity and MeasureJohn GarnettI. Analytic capacity
II. The Cauchy transform
III. Hausdorff measure
IV. Some examples
V. Applications to approximation
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Extremum Problems for Bounded Univalent Functions
Extremum Problems for Bounded Univalent FunctionsOlli TammiI. Generated functions
1. Introduction
2. Löwner-functions
3. Generalized Löwner-functions
4. A generalization of the class S(b)
5. Functions with bounded boundary rotation
II. Variation of the extremum function
1. Variation of Green's function
2. The Schiffer-condition for S(b)-functions
3. The coefficient a3
III. The area principle
1. The power inequality
2. Application to the coefficient a3 and a4
3. Optimization of parameters for...
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Topics in Nevanlinna Theory
Topics in Nevanlinna TheorySerge Lang, William CherryI. Nevanlinna theory in one variable
II. Equidimensional higher dimensional theory
III. Nevanlinna Theory for Meromorphic Functions on Coverings of C
IV. Equidimensional Nevanlinna Theory on Coverings of Cn
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Conformal Geometry and Quasiregular Mappings
Conformal Geometry and Quasiregular MappingsMatti VuorinenI. Conformal geometry
II. Modulus and capacity
III. Quasiregular mappings
IV. Boundary behavior
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Diophantine Approximations and Value Distribution Theory
Diophantine Approximations and Value Distribution TheoryPaul Vojta1. Heights and Integral Points
2. Diophantine Approximations
3. A Correspondence with Nevanlinna Theory
4. Consequences of the Main Conjecture
5. The Ramification Term
6. Approximation to Hyperplanes
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Classification Theory of Riemannian Manifolds
Classification Theory of Riemannian ManifoldsLeo Sario, Mitsuru Nakai, Cecilia Wang, Lung Ock ChungPreface and historical note
O. Laplace-Beltrami operator
I. Harmonic functions
II. Quasiharmonic functions
III. Bounded biharmonic functions
IV. Dirichlet finite biharmonic functions
V. Bounded Dirichlet finite biharmonic functions
VI. Harmonic, quasiharmonic, and biharmonic degeneracies
VII. Riesz representation of biharmonic functions
VIII. Biharmonic Green’s function γ
IX. Biharmonic Green’...
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Quasiconformal Mappings in the Plane
Quasiconformal Mappings in the PlaneJulian Ławrynowicz, Jan KrzyzI. Basic concepts and theorems in the analytic theory of quasiconformal mappings
II. The parametrical methods
III. A review of variational methods and basic applications in electrical engineering
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Integral Operators in Potential Theory
Integral Operators in Potential TheoryJosef Král1. Weak normal derivatives of potentials
2. Double layer potentials
3. Contractivity of Neumann's operator
4. Fredholm radius of the Neumann operator
5. Boundary value problems
6. Comments and references
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Dirichlet Integrals on Harmonic Spaces
Dirichlet Integrals on Harmonic SpacesFumi-Yuki Maeda1. Harmonic spaces
2. Superharmonic functions and potentials
3. Gradient measures
4. Self-adjoint harmonic spaces and Green potentials
5. Energy-finite harmonic functions and Green's formula
6. Spaces of Dirichlet-finite and Energy-finite Functions on Self-adjoint Harmonic Spaces
7. Functional completion
8. Royden boundary
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Abstract Analytic Function Theory and Hardy Algebras
Abstract Analytic Function Theory and Hardy AlgebrasKlaus Barbey, Heinz KönigI. Boundary value theory for harmonic and holomorphic functions in the unit disk
II. Function algebras: The bounded-measurable situation
III. Function algebras: The compact-continuous situation
IV. The abstract Hardy algebra situation
V. Elements of abstract Hardy algebra theory
VI. The abstract conjugation
VII. Analytic disks and isomorphisms with the unit disk situation
VIII. Weak compactness of M
IX. Logmodular dens...
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Analytically Uniform Spaces and their Applications to Convolution Equations
Analytically Uniform Spaces and their Applications to Convolution EquationsCarlos A. Berenstein, Milos A. DostalI. Definition and basic properties of analytically uniform spaces
II. Examples of AU-spaces
III. Spaces of approximate solutions to certain convolution equations
IV. The fundamental principle
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Lectures on n-Dimensional Quasiconformal Mappings
Lectures on n-Dimensional Quasiconformal MappingsJussi Väisälä1. The modulus of a curve family
2. Quasiconformal mappings
3. Background in real analysis
4. The analytic properties of quasiconformal mappings
5. Mapping problems
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Singular Integrals
Singular IntegralsUmberto NeriPart I. Singular Integrals: An Introduction
I. Convolutions
II. Fourier transforms
III. The Hilbert Transform
IV. Singular integrals in En
Part II. Singular Integral Operators and Distributions
I. Distributions and Fourier transforms
II. Singular integrals and Sobolev spaces
III. Spherical harmonics
IV. Singular integral operators
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On the Pointwise Convergence of Fourier Series
On the Pointwise Convergence of Fourier SeriesCharles J. Mozzochi1. A theorem of Stein and Weiss
2. The main theorem
3. A proof of theorem (2.2)
4. A proof of theorem (3.6)
5. A proof of theorem (4.2)
6. A proof of theorem (5.2)
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