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Adaptive Wavelet BEM for Boundary Integral Equations: Theory and Numerical Experiments

Numerical Functional Analysis and Optimization, ISSN 0163-0563, 01/2018, Volume 39, Issue 2, pp. 208 - 232

We are concerned with the numerical treatment of boundary integral equations by the adaptive wavelet boundary element method. In particular, we consider the...

manifolds | Adaptive wavelet BEM | 30H25 | regularity | weighted Sobolev spaces | Besov spaces | integral equations | 45E99 | double layer potential operator | 47B38 | 46E35 | 42C40 | non-linear approximation | 35B65 | 65T60 | MATHEMATICS, APPLIED | APPROXIMATION | ELEMENT METHOD | PART II | LIPSCHITZ-DOMAINS | ELLIPTIC PROBLEMS | DECOMPOSITIONS | OPERATOR-EQUATIONS | DIRICHLET PROBLEM | BESOV REGULARITY | CONVERGENCE-RATES | Operators (mathematics) | Wavelet | Boundary integral method | Mathematical analysis | Integral equations | Boundary element method

manifolds | Adaptive wavelet BEM | 30H25 | regularity | weighted Sobolev spaces | Besov spaces | integral equations | 45E99 | double layer potential operator | 47B38 | 46E35 | 42C40 | non-linear approximation | 35B65 | 65T60 | MATHEMATICS, APPLIED | APPROXIMATION | ELEMENT METHOD | PART II | LIPSCHITZ-DOMAINS | ELLIPTIC PROBLEMS | DECOMPOSITIONS | OPERATOR-EQUATIONS | DIRICHLET PROBLEM | BESOV REGULARITY | CONVERGENCE-RATES | Operators (mathematics) | Wavelet | Boundary integral method | Mathematical analysis | Integral equations | Boundary element method

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 11/2018, Volume 12, Issue 8, pp. 1845 - 1875

We investigate the relation between analytic Campanato spaces $$\mathcal {AL}_{p,s}$$ ALp,s and the spaces F(p, q, s), characterize the bounded and compact...

47B07 | Operator Theory | Analysis | Primary 30H25 | 30H80 | Riemann–Stieltjes operators | 30H35 | Mathematics, general | Corona theorem | Mathematics | Analytic Campanato spaces | Interpolating sequences | MATHEMATICS | MATHEMATICS, APPLIED | CARLESON MEASURES | MULTIPLIERS | Riemann-Stieltjes operators | FAMILY | Bisphenol-A | Yuan (China)

47B07 | Operator Theory | Analysis | Primary 30H25 | 30H80 | Riemann–Stieltjes operators | 30H35 | Mathematics, general | Corona theorem | Mathematics | Analytic Campanato spaces | Interpolating sequences | MATHEMATICS | MATHEMATICS, APPLIED | CARLESON MEASURES | MULTIPLIERS | Riemann-Stieltjes operators | FAMILY | Bisphenol-A | Yuan (China)

Journal Article

Afrika Matematika, ISSN 1012-9405, 6/2016, Volume 27, Issue 3, pp. 603 - 615

In this paper, the S-transform of derivatives and derivatives of S-transform are obtained. The characterization of Besov and weighted Besov spaces in terms of...

65R10 | Mathematics, general | Mathematics Education | Fourier transform | Mathematics | History of Mathematical Sciences | Applications of Mathematics | 30H25 | S-Transform | Besov space

65R10 | Mathematics, general | Mathematics Education | Fourier transform | Mathematics | History of Mathematical Sciences | Applications of Mathematics | 30H25 | S-Transform | Besov space

Journal Article

Advances in Nonlinear Analysis, ISSN 2191-9496, 01/2017, Volume 8, Issue 1, pp. 203 - 224

As an essential extension of the well known case to the hyper-dissipative case , this paper establishes both well-posedness and ill-posedness (not only norm...

46E35 | generalized Carleson measure spaces | Incompressible Navier–Stokes system with dissipation | 30H25 | 35Q30 | 31C15 | 42B37 | well/ill-posedness for mild solutions | Incompressible Navier-Stokes system with dissipation | MATHEMATICS, APPLIED | FRACTIONAL SOBOLEV SPACE | NORM INFLATION | EQUATIONS | LIMIT | ILL-POSEDNESS | UNIQUENESS | MATHEMATICS | HOMOTHETIC VARIANT | DIFFUSION | MILD SOLUTIONS

46E35 | generalized Carleson measure spaces | Incompressible Navier–Stokes system with dissipation | 30H25 | 35Q30 | 31C15 | 42B37 | well/ill-posedness for mild solutions | Incompressible Navier-Stokes system with dissipation | MATHEMATICS, APPLIED | FRACTIONAL SOBOLEV SPACE | NORM INFLATION | EQUATIONS | LIMIT | ILL-POSEDNESS | UNIQUENESS | MATHEMATICS | HOMOTHETIC VARIANT | DIFFUSION | MILD SOLUTIONS

Journal Article

Annals of Functional Analysis, ISSN 2008-8752, 2015, Volume 6, Issue 3, pp. 1 - 7

Journal Article

Mathematics of Control, Signals, and Systems, ISSN 0932-4194, 9/2017, Volume 29, Issue 3, pp. 1 - 21

In this paper, we will establish necessary and sufficient conditions for a Laplace–Carleson embedding to be bounded for certain spaces of functions on the...

Semigroup system | Admissibility | Carleson measure | Systems Theory, Control | Mathematics | 30H25 | 30H20 | Besov spaces | Laplace–Carleson embedding | Control, Robotics, Mechatronics | 93B28 | 47A57 | Linear evolution equation | Communications Engineering, Networks | Laplace transform | LINEAR-SYSTEMS | MEASURE CRITERION | SPACES | Laplace-Carleson embedding | ENGINEERING, ELECTRICAL & ELECTRONIC | SEMIGROUPS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | OBSERVATION OPERATORS | AUTOMATION & CONTROL SYSTEMS | Boundary conditions | Operators | Criteria

Semigroup system | Admissibility | Carleson measure | Systems Theory, Control | Mathematics | 30H25 | 30H20 | Besov spaces | Laplace–Carleson embedding | Control, Robotics, Mechatronics | 93B28 | 47A57 | Linear evolution equation | Communications Engineering, Networks | Laplace transform | LINEAR-SYSTEMS | MEASURE CRITERION | SPACES | Laplace-Carleson embedding | ENGINEERING, ELECTRICAL & ELECTRONIC | SEMIGROUPS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | OBSERVATION OPERATORS | AUTOMATION & CONTROL SYSTEMS | Boundary conditions | Operators | Criteria

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 4/2014, Volume 24, Issue 2, pp. 649 - 666

This note characterizes both boundedness and compactness of a composition operator between any two analytic Campanato spaces on the unit complex disk.

Compactness | Composition operator | Boundedness | 30H35 | 47B33 | Mathematics | 30H25 | 30H10 | Abstract Harmonic Analysis | 46E15 | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Analytic Campanato space | Differential Geometry | Dynamical Systems and Ergodic Theory | MATHEMATICS | BMOA | BLOCH SPACE | COMPACT COMPOSITION OPERATORS

Compactness | Composition operator | Boundedness | 30H35 | 47B33 | Mathematics | 30H25 | 30H10 | Abstract Harmonic Analysis | 46E15 | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Analytic Campanato space | Differential Geometry | Dynamical Systems and Ergodic Theory | MATHEMATICS | BMOA | BLOCH SPACE | COMPACT COMPOSITION OPERATORS

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 4/2017, Volume 27, Issue 2, pp. 1013 - 1028

On the unit disk we introduce a new class of tent spaces $$T^q_{s,t}(\mu )$$ T s , t q ( μ ) for any positive Borel measure $$\mu $$ μ , consider a class of...

Carleson measure | Tent spaces | 30H35 | Embedding | Mathematics | 30H25 | 30H30 | Abstract Harmonic Analysis | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | Möbius invariant spaces | MATHEMATICS | Mobius invariant spaces | CARLESON MEASURES

Carleson measure | Tent spaces | 30H35 | Embedding | Mathematics | 30H25 | 30H30 | Abstract Harmonic Analysis | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | Möbius invariant spaces | MATHEMATICS | Mobius invariant spaces | CARLESON MEASURES

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 3/2014, Volume 102, Issue 3, pp. 263 - 270

We consider the minimal Möbius invariant space of the unit disk with norm defined in terms of the second derivative. We obtain the best constant for the...

32A25 | Minimal Möbius invariant space | Operator norm | Mathematics, general | Mathematics | 30H25 | Bergman projection | Besov space | Minimal Mobius invariant space | MATHEMATICS | BLOCH SPACE | NORM ESTIMATE | BESOV-SPACES | L-P SPACES

32A25 | Minimal Möbius invariant space | Operator norm | Mathematics, general | Mathematics | 30H25 | Bergman projection | Besov space | Minimal Mobius invariant space | MATHEMATICS | BLOCH SPACE | NORM ESTIMATE | BESOV-SPACES | L-P SPACES

Journal Article

Complex Variables and Elliptic Equations, ISSN 1747-6933, 10/2015, Volume 60, Issue 10, pp. 1327 - 1345

In this paper, we establish an analytic version of critical spaces on unit disc , denoted by . Further, we prove a relation between and Morrey spaces. By the...

47B38 | Carleson measure | fractional derivative | multipliers | 30H25 | critical analytic Q-space | Morrey space | MATHEMATICS | CARLESON MEASURES | THEOREMS | Discs | Operators | Multipliers | Integrals | Mathematical analysis | Images | Complex variables

47B38 | Carleson measure | fractional derivative | multipliers | 30H25 | critical analytic Q-space | Morrey space | MATHEMATICS | CARLESON MEASURES | THEOREMS | Discs | Operators | Multipliers | Integrals | Mathematical analysis | Images | Complex variables

Journal Article

Boletín de la Sociedad Matemática Mexicana, ISSN 1405-213X, 10/2015, Volume 21, Issue 2, pp. 171 - 188

We introduce the hyperbolic $$F^*_{g}(p,q,s) $$ F g ∗ ( p , q , s ) and $$F^*_{\varphi }( p,q,s) $$ F φ ∗ ( p , q , s ) classes of holomorphic functions...

Mathematics, general | Mathematics | 30H25 | F(p, q, s)$$ F ( p , q , s ) spaces | 30D50 | Hyperbolic Q -classes

Mathematics, general | Mathematics | 30H25 | F(p, q, s)$$ F ( p , q , s ) spaces | 30D50 | Hyperbolic Q -classes

Journal Article

Applicable Analysis, ISSN 0003-6811, 01/2016, Volume 95, Issue 1, pp. 78 - 96

In this paper, we consider the Cauchy problem for the 2D viscous shallow water system in , . We first prove the local well-posedness of this problem by using...

global existence | local well-posedness | 42B25 | 49K40 | the Littlewood-Paley theory | 35A01 | 35B44 | the 2D viscous shallow water system | 30H25 | Sobolev spaces | the Littlewood–Paley theory | MATHEMATICS, APPLIED | EQUATIONS | CAUCHY-PROBLEM | MODEL

global existence | local well-posedness | 42B25 | 49K40 | the Littlewood-Paley theory | 35A01 | 35B44 | the 2D viscous shallow water system | 30H25 | Sobolev spaces | the Littlewood–Paley theory | MATHEMATICS, APPLIED | EQUATIONS | CAUCHY-PROBLEM | MODEL

Journal Article

Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2016, Volume 68, Issue 1, pp. 383 - 403

We compute the norm of some bilinear forms on products of weighted Besov spaces in terms of the norm of their symbol in a space of pointwise multipliers...

Hankel operators | Bilinear forms | Weak products | Weighted Besov spaces | weighted Besov spaces | MATHEMATICS | CARLESON MEASURES | MULTIPLIERS | bilinear forms | DIRICHLET | weak products

Hankel operators | Bilinear forms | Weak products | Weighted Besov spaces | weighted Besov spaces | MATHEMATICS | CARLESON MEASURES | MULTIPLIERS | bilinear forms | DIRICHLET | weak products

Journal Article

Complex Variables and Elliptic Equations, ISSN 1747-6933, 06/2016, Volume 61, Issue 6, pp. 761 - 771

Given , , let denote the Besov type space of analytic functions on the unit disk . Allen, Heller and Pons have shown that the isometries among composition...

composition operator | 47B38 | 46B04 | isometries | 46E20 | 47B33 | Besov type space | 30H25 | 30H20 | Besov space | 30H10 | MATHEMATICS | BANACH-SPACES | Game theory | Operators | Analytic functions | Mathematical analysis | Symbols | Images | Dirichlet problem | Disks | Complex variables

composition operator | 47B38 | 46B04 | isometries | 46E20 | 47B33 | Besov type space | 30H25 | 30H20 | Besov space | 30H10 | MATHEMATICS | BANACH-SPACES | Game theory | Operators | Analytic functions | Mathematical analysis | Symbols | Images | Dirichlet problem | Disks | Complex variables

Journal Article

Potential Analysis, ISSN 0926-2601, 8/2014, Volume 41, Issue 2, pp. 543 - 553

On the unit ball of ℂ n , the space of those holomorphic functions satisfying mean Lipschitz condition $$ \int_0^1 \omega^*_p(t, f)^q \frac{dt}{t^{1+ q}}...

Geometry | Mean modulus of continuity | Potential Theory | Functional Analysis | Zygmund class | Probability Theory and Stochastic Processes | 32A30 | Mathematics | Mean Lipschitz condition | 30H25 | Besov space

Geometry | Mean modulus of continuity | Potential Theory | Functional Analysis | Zygmund class | Probability Theory and Stochastic Processes | 32A30 | Mathematics | Mean Lipschitz condition | 30H25 | Besov space

Journal Article

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, ISSN 1370-1444, 10/2014, Volume 21, Issue 4, pp. 759 - 767

The Hilbert-Schmidtness of composition operators acting between the classical Hilbert Hardy space and the Dirichlet space is known. We here consider...

MATHEMATICS | composition operator | Hardy spaces | COMPACT COMPOSITION OPERATORS | Dirichlet space | SCHMIDT COMPOSITION OPERATORS | DERIVATIVES | BERGMAN SPACES | Banach spaces | Research | Mathematical research | Operator theory | 47B33 | 30H25 | 30H10

MATHEMATICS | composition operator | Hardy spaces | COMPACT COMPOSITION OPERATORS | Dirichlet space | SCHMIDT COMPOSITION OPERATORS | DERIVATIVES | BERGMAN SPACES | Banach spaces | Research | Mathematical research | Operator theory | 47B33 | 30H25 | 30H10

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 6/2014, Volume 8, Issue 5, pp. 1077 - 1086

In this paper, we show that if a function $$f$$ f in the $$Q_p$$ Q p space with $$0

46E15 | Operator Theory | 47A16 | Analysis | Univalent functions | Mathematics, general | Mathematics | 30H25 | Q_p$$ Q p spaces | Cyclic vectors

Journal Article

Foundations of Computational Mathematics, ISSN 1615-3375, 12/2015, Volume 15, Issue 6, pp. 1533 - 1569

We study regularity properties of solutions to operator equations on patchwise smooth manifolds $$\partial \Omega $$ ∂ Ω , e.g., boundaries of polyhedral...

Linear and Multilinear Algebras, Matrix Theory | Double layer | Mathematics | 30H25 | Besov spaces | Manifolds | Wavelets | 45E99 | 47B38 | Adaptive methods | 46E35 | Integral equations | 42C40 | Numerical Analysis | 35B65 | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Economics, general | Regularity | 65T60 | Weighted Sobolev spaces | Nonlinear approximation | MATHEMATICS, APPLIED | BASES | APPROXIMATION | ELEMENT METHOD | INTERPOLATION | MATHEMATICS | ADAPTIVE WAVELET METHODS | ELLIPTIC PROBLEMS | DIRICHLET PROBLEM | COMPUTER SCIENCE, THEORY & METHODS | TRIEBEL-LIZORKIN SPACES | SCHEMES | Manifolds (Mathematics) | Transformations (Mathematics) | Analysis

Linear and Multilinear Algebras, Matrix Theory | Double layer | Mathematics | 30H25 | Besov spaces | Manifolds | Wavelets | 45E99 | 47B38 | Adaptive methods | 46E35 | Integral equations | 42C40 | Numerical Analysis | 35B65 | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Economics, general | Regularity | 65T60 | Weighted Sobolev spaces | Nonlinear approximation | MATHEMATICS, APPLIED | BASES | APPROXIMATION | ELEMENT METHOD | INTERPOLATION | MATHEMATICS | ADAPTIVE WAVELET METHODS | ELLIPTIC PROBLEMS | DIRICHLET PROBLEM | COMPUTER SCIENCE, THEORY & METHODS | TRIEBEL-LIZORKIN SPACES | SCHEMES | Manifolds (Mathematics) | Transformations (Mathematics) | Analysis

Journal Article

Numerical Functional Analysis and Optimization: Operator Algebras and Representation Theory: Frames, Wavelets, and Fractals, ISSN 0163-0563, 07/2012, Volume 33, Issue 7-9, pp. 847 - 871

Function spaces are central topics in analysis. Often those spaces and related analysis involves symmetries in form of an action of a Lie group. Coorbit theory...

Coorbit spaces | Stratified Lie group | Primary 30H25 | Sub-Laplacian | Sampling | Secondary 46E35, 43A15 | Besov spaces | MATHEMATICS, APPLIED | INTEGRABLE GROUP-REPRESENTATIONS | FRAMES | BANACH-SPACES | NILPOTENT LIE-GROUPS

Coorbit spaces | Stratified Lie group | Primary 30H25 | Sub-Laplacian | Sampling | Secondary 46E35, 43A15 | Besov spaces | MATHEMATICS, APPLIED | INTEGRABLE GROUP-REPRESENTATIONS | FRAMES | BANACH-SPACES | NILPOTENT LIE-GROUPS

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 9/2014, Volume 17, Issue 3, pp. 897 - 906

Let $$\mathbb{D}$$ stand for the unit disc in the complex plane ℂ. Given 0 < p < ∞, −1 < λ < ∞, the analytic weighted Besov space $$B_p^\lambda \left(...

Abstract Harmonic Analysis | Functional Analysis | Secondary 47G20 | Analysis | Primary 30H25 | Mathematics | analytic Besov space | fraction integro-differentiation | Integral Transforms, Operational Calculus | BOUNDED SYMMETRICAL DOMAINS | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | LIPSCHITZ SPACES

Abstract Harmonic Analysis | Functional Analysis | Secondary 47G20 | Analysis | Primary 30H25 | Mathematics | analytic Besov space | fraction integro-differentiation | Integral Transforms, Operational Calculus | BOUNDED SYMMETRICAL DOMAINS | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | LIPSCHITZ SPACES

Journal Article

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