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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
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
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
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
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
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
Journal Article
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, ISSN 0022-247X, 09/2016, Volume 441, Issue 1, pp. 57 - 103
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
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
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
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
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
Journal Article
ANALYSIS AND MATHEMATICAL PHYSICS, ISSN 1664-2368, 03/2020, Volume 10, Issue 1
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
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
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
Journal Article
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
Journal Article
Journal of Pseudo-Differential Operators and Applications, ISSN 1662-9981, 12/2019, Volume 10, Issue 4, pp. 999 - 1014
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
Journal Article
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