2019, Communications and control engineering, ISBN 9783030124809, 605

Control of Wave and Beam PDEs is a concise, self-contained introduction to Riesz bases in Hilbert space and their applications to control systems described by...

Riesz spaces | Control and Systems Theory | Engineering | Systems Theory, Control | Partial Differential Equations

Riesz spaces | Control and Systems Theory | Engineering | Systems Theory, Control | Partial Differential Equations

eBook

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, 02/2015, Volume 471, Issue 2174, p. 20140642

We improve the currently known thresholds for basisness of the family of periodically dilated p,q-sine functions. Our findings rely on a Beurling decomposition...

Generalized trigonometric functions | Riesz basis | Schauder basis | generalized trigonometric functions | P-LAPLACIAN | MULTIDISCIPLINARY SCIENCES | 1008 | 1440

Generalized trigonometric functions | Riesz basis | Schauder basis | generalized trigonometric functions | P-LAPLACIAN | MULTIDISCIPLINARY SCIENCES | 1008 | 1440

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2018, Volume 56, Issue 5, pp. 3010 - 3039

The fractional Laplacian Delta(beta/2) is the generator of the beta-stable Levy process, which is the scaling limit of the Levy flight. Due to the divergence...

Galerkin schemes | B-spline and Riesz basis | Tempered fractional Laplacian | Preconditioning | pre-conditioning | MATHEMATICS, APPLIED | SPLINE-WAVELETS | APPROXIMATION | REGULARITY | tempered fractional Laplacian | GUIDE | NONLOCAL DIFFUSION-PROBLEMS | SCHEMES | Mathematics - Numerical Analysis

Galerkin schemes | B-spline and Riesz basis | Tempered fractional Laplacian | Preconditioning | pre-conditioning | MATHEMATICS, APPLIED | SPLINE-WAVELETS | APPROXIMATION | REGULARITY | tempered fractional Laplacian | GUIDE | NONLOCAL DIFFUSION-PROBLEMS | SCHEMES | Mathematics - Numerical Analysis

Journal Article

International Journal of Wavelets, Multiresolution and Information Processing, ISSN 0219-6913, 07/2018, Volume 16, Issue 4

In this paper, continuous piecewise quadratic finite element wavelets are constructed on general polygons in R-2. The wavelets are stable in H-s for vertical...

vanishing moments | Wavelets | Riesz bases | biorthogonality | finite elements | BASES | GENERAL MESHES | STABILITY | PREWAVELETS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | CONSTRUCTION | TRIANGULATIONS

vanishing moments | Wavelets | Riesz bases | biorthogonality | finite elements | BASES | GENERAL MESHES | STABILITY | PREWAVELETS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | CONSTRUCTION | TRIANGULATIONS

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2010, Volume 249, Issue 10, pp. 2397 - 2408

Given a Hilbert space and the generator of a strongly continuous group on this Hilbert space. If the eigenvalues of the generator have a uniform gap, and if...

Riesz family | Semigroup | Riesz basis | MSC-46C10 | MSC-47D06 | MATHEMATICS

Riesz family | Semigroup | Riesz basis | MSC-46C10 | MSC-47D06 | MATHEMATICS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2016, Volume 441, Issue 1, pp. 57 - 103

The paper is concerned with the Riesz basis property of a boundary value problem associated in L2[0,1]⊗C2 with the following 2×2 Dirac type...

Transformation operators | Systems of ordinary differential equations | Regular boundary conditions | Riesz basis property | Timoshenko beam model

Transformation operators | Systems of ordinary differential equations | Regular boundary conditions | Riesz basis property | Timoshenko beam model

Journal Article

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, ISSN 0022-247X, 09/2016, Volume 441, Issue 1, pp. 57 - 103

The paper is concerned with the Riesz basis property of a boundary value problem associated in L-2[0,1] circle times C-2 with the following 2 x 2 Dirac type...

TIMOSHENKO BEAM | MATHEMATICS, APPLIED | BASES | Riesz basis property | SPECTRAL DECOMPOSITIONS | COMPLETENESS | SELF-ADJOINT OPERATOR | POTENTIALS | Timoshenko beam model | REGULAR BOUNDARY-CONDITIONS | 1ST-ORDER SYSTEMS | MATHEMATICS | Transformation operators | Systems of ordinary differential equations | Regular boundary conditions | EXPANSION | LINEAR-DIFFERENTIAL EQUATIONS | Differential equations

TIMOSHENKO BEAM | MATHEMATICS, APPLIED | BASES | Riesz basis property | SPECTRAL DECOMPOSITIONS | COMPLETENESS | SELF-ADJOINT OPERATOR | POTENTIALS | Timoshenko beam model | REGULAR BOUNDARY-CONDITIONS | 1ST-ORDER SYSTEMS | MATHEMATICS | Transformation operators | Systems of ordinary differential equations | Regular boundary conditions | EXPANSION | LINEAR-DIFFERENTIAL EQUATIONS | Differential equations

Journal Article

Applied Numerical Mathematics, ISSN 0168-9274, 10/2019, Volume 144, pp. 59 - 82

The radial basis functions collocation method is developed to solve Riesz space fractional advection-dispersion equation (RSFADE). To do this, we first provide...

Radial basis functions | Riesz space fractional advection-dispersion equation | Riemann-Liouville fractional derivatives | Meshless method | INTERPOLATION | MATHEMATICS, APPLIED | ELEMENT SOLUTION | REPRODUCING KERNEL-METHOD | ANOMALOUS TRANSPORT | DYNAMICS | DIFFUSION | FINITE-DIFFERENCE APPROXIMATIONS

Radial basis functions | Riesz space fractional advection-dispersion equation | Riemann-Liouville fractional derivatives | Meshless method | INTERPOLATION | MATHEMATICS, APPLIED | ELEMENT SOLUTION | REPRODUCING KERNEL-METHOD | ANOMALOUS TRANSPORT | DYNAMICS | DIFFUSION | FINITE-DIFFERENCE APPROXIMATIONS

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 07/2012, Volume 253, Issue 2, pp. 400 - 437

Under the assumption that V∈L2([0,π];dx), we derive necessary and sufficient conditions in terms of spectral data for (non-self-adjoint) Schrödinger operators...

Periodic and antiperiodic boundary conditions | Riesz basis | Non-self-adjoint Hill operators | Secondary | Primary | BASIS PROPERTY | STURM-LIOUVILLE OPERATOR | ROOT FUNCTIONS | SPECTRAL DECOMPOSITIONS | SCALAR TYPE | ORDINARY DIFFERENTIAL-OPERATORS | POTENTIALS | HILL OPERATORS | MATHEMATICS | ALGEBRO-GEOMETRIC SOLUTIONS | EQUATION

Periodic and antiperiodic boundary conditions | Riesz basis | Non-self-adjoint Hill operators | Secondary | Primary | BASIS PROPERTY | STURM-LIOUVILLE OPERATOR | ROOT FUNCTIONS | SPECTRAL DECOMPOSITIONS | SCALAR TYPE | ORDINARY DIFFERENTIAL-OPERATORS | POTENTIALS | HILL OPERATORS | MATHEMATICS | ALGEBRO-GEOMETRIC SOLUTIONS | EQUATION

Journal Article

Journal of Applied Analysis, ISSN 1425-6908, 06/2019, Volume 25, Issue 1, pp. 13 - 23

This paper studies a linear hyperbolic system with boundary conditions that was first studied under some weaker conditions in [ , ]. Problems on the expansion...

15A42 | Hyperbolic system | eigenvalues | 46B15 | sine-type function | eigenvectors | 46A35 | 47A55 | 65F15 | 65H17 | Riesz basis | Mathematical analysis | Boundary conditions | Eigen values

15A42 | Hyperbolic system | eigenvalues | 46B15 | sine-type function | eigenvectors | 46A35 | 47A55 | 65F15 | 65H17 | Riesz basis | Mathematical analysis | Boundary conditions | Eigen values

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2013, Volume 405, Issue 2, pp. 453 - 465

The Hill operators Ly=−y″+v(x)y, considered with complex valued π-periodic potentials v and subject to periodic, antiperiodic or Neumann boundary conditions...

Potential smoothness | Hill operator | Riesz bases | MATHEMATICS | MATHEMATICS, APPLIED | DIRAC OPERATORS | GAPS | INSTABILITY ZONES

Potential smoothness | Hill operator | Riesz bases | MATHEMATICS | MATHEMATICS, APPLIED | DIRAC OPERATORS | GAPS | INSTABILITY ZONES

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 02/2017, Volume 272, Issue 3, pp. 1017 - 1043

Some special Hilbert spaces are introduced to present the class of infinitesimal operators with complete minimal non-basis family of eigenvectors. The discrete...

Hardy inequality | [formula omitted]-group | Riesz basis | Symmetric basis | group | HILBERT | MATHEMATICS | THEOREM | SPACES | STRONGLY CONTINUOUS-GROUPS | C-0-group | Equality

Hardy inequality | [formula omitted]-group | Riesz basis | Symmetric basis | group | HILBERT | MATHEMATICS | THEOREM | SPACES | STRONGLY CONTINUOUS-GROUPS | C-0-group | Equality

Journal Article

ANALYSIS AND MATHEMATICAL PHYSICS, ISSN 1664-2368, 03/2020, Volume 10, Issue 1

We establish a criterion for a set of eigenfunctions of the one-dimensional Schrodinger operator with distributional potentials and boundary conditions...

Distributional potential | MATHEMATICS | MATHEMATICS, APPLIED | Boundary conditions dependent on the eigenvalue parameter | One-dimensional Schrodinger equation | Sturm-Liouville operator | Riesz basis | L-P | Singular potential | SPECTRAL PARAMETER | Mathematics | Spectral Theory | Functional Analysis | Mathematical Physics | Classical Analysis and ODEs

Distributional potential | MATHEMATICS | MATHEMATICS, APPLIED | Boundary conditions dependent on the eigenvalue parameter | One-dimensional Schrodinger equation | Sturm-Liouville operator | Riesz basis | L-P | Singular potential | SPECTRAL PARAMETER | Mathematics | Spectral Theory | Functional Analysis | Mathematical Physics | Classical Analysis and ODEs

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2017, Volume 447, Issue 1, pp. 84 - 108

The one-dimensional Dirac operator with periodic potential V=(0P(x)Q(x)0), where P,Q∈L2([0,π]) subject to periodic, antiperiodic or a general strictly regular...

Potential smoothness | Dirac operator | Riesz basis property | SCHRODINGER OPERATOR | MATHEMATICS | ZAKHAROV-SHABAT SYSTEM | MATHEMATICS, APPLIED | DIRICHLET EIGENVALUES | ADJOINT HILLS OPERATORS | INSTABILITY ZONES

Potential smoothness | Dirac operator | Riesz basis property | SCHRODINGER OPERATOR | MATHEMATICS | ZAKHAROV-SHABAT SYSTEM | MATHEMATICS, APPLIED | DIRICHLET EIGENVALUES | ADJOINT HILLS OPERATORS | INSTABILITY ZONES

Journal Article

Functional Analysis and Its Applications, ISSN 0016-2663, 7/2019, Volume 53, Issue 3, pp. 192 - 204

Let T be a self-adjoint operator on a Hilbert space H with domain $$\mathscr{D}(T)$$ D ( T ) . Assume that the spectrum of T is contained in the union of...

Mathematics | unconditional basis of subspaces | Functional Analysis | Analysis | Riesz basis | non-self-adjoint perturbations | MATHEMATICS | MATHEMATICS, APPLIED

Mathematics | unconditional basis of subspaces | Functional Analysis | Analysis | Riesz basis | non-self-adjoint perturbations | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

IEEE Transactions on Signal Processing, ISSN 1053-587X, 10/2014, Volume 62, Issue 20, pp. 5270 - 5281

Piecewise, low-order polynomial, Riesz basis families are constructed such that they share the same coefficient functionals of smoother, orthonormal bases in a...

Context | Dictionaries | basis construction | Dynamic range | Signal processing | Polynomials | Riesz bases | sparsity basis selection | Approximation methods | Fourier series | Optimization | ell_p regularization | ell-p regularization | SCHEME | DESIGN | MULTIPLICATION | l(p) regularization | WAVELET TRANSFORM | ALGORITHMS | FREQUENCY-ANALYSIS | ENGINEERING, ELECTRICAL & ELECTRONIC | Fourier analysis | Usage | Numerical analysis | Mathematical optimization | Innovations | Operators | Construction | Constraints | Equivalence | Mathematical models | Derivatives | Indexing

Context | Dictionaries | basis construction | Dynamic range | Signal processing | Polynomials | Riesz bases | sparsity basis selection | Approximation methods | Fourier series | Optimization | ell_p regularization | ell-p regularization | SCHEME | DESIGN | MULTIPLICATION | l(p) regularization | WAVELET TRANSFORM | ALGORITHMS | FREQUENCY-ANALYSIS | ENGINEERING, ELECTRICAL & ELECTRONIC | Fourier analysis | Usage | Numerical analysis | Mathematical optimization | Innovations | Operators | Construction | Constraints | Equivalence | Mathematical models | Derivatives | Indexing

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 12/2013, Volume 77, Issue 4, pp. 533 - 557

We consider a regular indefinite Sturm–Liouville eigenvalue problem −f′′ + q f = λ r f on [a, b] subject to general self-adjoint boundary conditions and with a...

Primary 34B09 | Secondary 34B24 | 26D10 | HELP inequality | Analysis | regular critical point | Mathematics | Indefinite Sturm–Liouville problem | 47B50 | 34L10 | Riesz basis | Indefinite Sturm-Liouville problem | MATHEMATICS | LITTLEWOOD | SIMILARITY PROBLEM | HARDY | OPERATORS

Primary 34B09 | Secondary 34B24 | 26D10 | HELP inequality | Analysis | regular critical point | Mathematics | Indefinite Sturm–Liouville problem | 47B50 | 34L10 | Riesz basis | Indefinite Sturm-Liouville problem | MATHEMATICS | LITTLEWOOD | SIMILARITY PROBLEM | HARDY | OPERATORS

Journal Article

18.
Full Text
On a necessary aspect for the Riesz basis property for indefinite Sturm‐Liouville problems

Mathematische Nachrichten, ISSN 0025-584X, 10/2014, Volume 287, Issue 14-15, pp. 1710 - 1732

In 1996, H. Volkmer observed that the inequality ∫−111|r||f′|2dx2≤K2∫−11|f|2dx∫−111rf′′2dxis satisfied with some positive constant K>0 for a certain class of...

34B24 | HELP inequality | 26D10 | indefinite Sturm‐Liouville problem | 47A75 | 47A10 | 34L10 | Riesz basis | LRG condition | Indefinite Sturm-Liouville problem | MATHEMATICS | INEQUALITIES | LITTLEWOOD | SIMILARITY PROBLEM | HARDY | OPERATORS | indefinite Sturm-Liouville problem

34B24 | HELP inequality | 26D10 | indefinite Sturm‐Liouville problem | 47A75 | 47A10 | 34L10 | Riesz basis | LRG condition | Indefinite Sturm-Liouville problem | MATHEMATICS | INEQUALITIES | LITTLEWOOD | SIMILARITY PROBLEM | HARDY | OPERATORS | indefinite Sturm-Liouville problem

Journal Article

19.
Full Text
On a Riesz basis of exponentials related to a family of analytic operators and application

Journal of Pseudo-Differential Operators and Applications, ISSN 1662-9981, 12/2019, Volume 10, Issue 4, pp. 999 - 1014

In this paper, we are interested by the perturbed operator $$\begin{aligned} T(\varepsilon ):=T_0+\varepsilon T_1 +\varepsilon ^2T_2+\cdots +\varepsilon ^k...

Operator Theory | Algebra | Functional Analysis | Analysis | Families of exponentials | Eigenvalues | Isolated point | Elastic membrane | Mathematics | Riesz bases | Applications of Mathematics | Partial Differential Equations | SOUND RADIATION | MATHEMATICS | MATHEMATICS, APPLIED | PERTURBATION METHOD | GENERALIZED EIGENVECTORS | VIBRATING STRUCTURE | PLATE | Sequences (Mathematics) | Functions, Exponential | Research | Mathematical research | Operator theory

Operator Theory | Algebra | Functional Analysis | Analysis | Families of exponentials | Eigenvalues | Isolated point | Elastic membrane | Mathematics | Riesz bases | Applications of Mathematics | Partial Differential Equations | SOUND RADIATION | MATHEMATICS | MATHEMATICS, APPLIED | PERTURBATION METHOD | GENERALIZED EIGENVECTORS | VIBRATING STRUCTURE | PLATE | Sequences (Mathematics) | Functions, Exponential | Research | Mathematical research | Operator theory

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 12/2018, Volume 15, Issue 6, pp. 1 - 16

In the present paper, we are mainly concerned with the existence of a Riesz basis related to the Gribov operator $$\begin{aligned} A^{*2}A^2+\varepsilon (A^* A...

Gribov operator | 47B25 | Eigenvalues | generalized eigenvectors | Mathematics, general | Mathematics | 34L10 | Riesz basis | MATHEMATICS | COMPACT | MATHEMATICS, APPLIED | VIBRATING STRUCTURE | RADIATION | UNCONDITIONAL BASIS

Gribov operator | 47B25 | Eigenvalues | generalized eigenvectors | Mathematics, general | Mathematics | 34L10 | Riesz basis | MATHEMATICS | COMPACT | MATHEMATICS, APPLIED | VIBRATING STRUCTURE | RADIATION | UNCONDITIONAL BASIS

Journal Article

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