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Some spectral properties of the streaming operator with general boundary conditions

Mohamed Boulanouar (2008)

Applications of Mathematics

This paper deals with the spectral study of the streaming operator with general boundary conditions defined by means of a boundary operator $K$ . We study the positivity and the irreducibility of the generated semigroup proved in [M. Boulanouar, L’opérateur d’Advection: existence d’un $C_{0}$ -semi-groupe (I), Transp. Theory Stat. Phys. 31, 2002, 153–167], in the case $∥ K ∥ \geq 1$ . We also give some spectral properties of the streaming operator and we characterize the type of the generated semigroup in terms of the...

Sous-ellipticité d'opérateurs intégro-différentiels vérifiant le principe du maximum

C. E. Cancelier, J. Y. Chemin (1990/1991)

Séminaire Équations aux dérivées partielles (Polytechnique)

Spectral analysis for a class of integral-difference operators: known facts, new results, and open problems.

Melnikov, Yuri B. (2004)

Discrete Dynamics in Nature and Society

Spectral analysis of subordinate Brownian motions on the half-line

Mateusz Kwaśnicki (2011)

Studia Mathematica

We study one-dimensional Lévy processes with Lévy-Khintchine exponent ψ(ξ²), where ψ is a complete Bernstein function. These processes are subordinate Brownian motions corresponding to subordinators whose Lévy measure has completely monotone density; or, equivalently, symmetric Lévy processes whose Lévy measure has completely monotone density on (0,∞). Examples include symmetric stable processes and relativistic processes. The main result is a formula for the generalized eigenfunctions of transition...

Spectral Asymmetrie and Zeta Functions.

Mariusz Wodzicki (1982)

Inventiones mathematicae

Spectral gap lower bound for the one-dimensional fractional Schrödinger operator in the interval

Kamil Kaleta (2012)

Studia Mathematica

We prove a uniform lower bound for the difference λ₂ - λ₁ between the first two eigenvalues of the fractional Schrödinger operator ${(- Δ)}^{α / 2} + V$ , α ∈ (1,2), with a symmetric single-well potential V in a bounded interval (a,b), which is related to the Feynman-Kac semigroup of the symmetric α-stable process killed upon leaving (a,b). “Uniform” means that the positive constant $C_{α}$ appearing in our estimate $λ ₂ - λ ₁ \geq C_{α} {(b - a)}^{- α}$ is independent of the potential V. In the general case of α ∈ (0,2), we also find a uniform lower bound for...

Spectral Invariance for Algebras of Pseudodifferential operators on Besov-Triebel-Lizorkin spaces.

Elmar Schrohe, Hans-Gern Leopold (1993)

Manuscripta mathematica

Spectral perturbations in linear viscoelasticity of the Boltzmann type

J. Cainzos, M. Lobo-Hidalgo (1985)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Spectral properties of non-local uniformly-elliptic operators.

Davidson, Fordyce A., Dodds, Niall (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Spectral Properties of the Cauchy Operator and the Operator of Logarithmic Potential Type on L2 Space With Radial Weight

Milutin Dostanić (1998)

Matematički Vesnik

Spectral theory of SG pseudo-differential operators on $L^{p} (ℝ ⁿ)$

Aparajita Dasgupta, M. W. Wong (2008)

Studia Mathematica

To every elliptic SG pseudo-differential operator with positive orders, we associate the minimal and maximal operators on $L^{p} (ℝ ⁿ)$ , 1 < p < ∞, and prove that they are equal. The domain of the minimal ( = maximal) operator is explicitly computed in terms of a Sobolev space. We prove that an elliptic SG pseudo-differential operator is Fredholm. The essential spectra of elliptic SG pseudo-differential operators with positive orders and bounded SG pseudo-differential operators with orders 0,0 are computed....

Spectre du noyau intégral ${(x^{2} + y^{2} + 1)}^{- 1}$

Michel Gaudin (1981)

Annales de l'institut Fourier

On construit les fonctions propres sur $R$ et les valeurs caractéristiques $λ_{n}$ du noyau de Hilbert-Schmidt $(x^{2} + y^{2} + 1)^{- 1}$ . Le spectre est donné par la solution d’une équation transcendante dont le comportement asymptotique est $λ_{n} ≃ \frac{1}{2} exp (π \sqrt{n})$ .

Stability of a spline collocation method for strongly elliptic multidimensional singular integral equations.

R. Schneider (1990/1991)

Numerische Mathematik

Strong and weak stability of some Markov operators

Ryszard Rudnicki (2000)

Colloquium Mathematicae

An integral Markov operator $P$ appearing in biomathematics is investigated. This operator acts on the space of probabilistic Borel measures. Let $μ$ and $ν$ be probabilistic Borel measures. Sufficient conditions for weak and strong convergence of the sequence $(P^{n} μ - P^{n} ν)$ to $0$ are given.

Subalgebras to a Wiener type algebra of pseudo-differential operators

Joachim Toft (2001)

Annales de l’institut Fourier

We study general continuity properties for an increasing family of Banach spaces $S_{w}^{p}$ of classes for pseudo-differential symbols, where $S_{w}^{\infty} = S_{w}$ was introduced by J. Sjöstrand in 1993. We prove that the operators in $Op (S_{w}^{p})$ are Schatten-von Neumann operators of order $p$ on $L^{2}$ . We prove also that $Op (S_{w}^{p}) Op (S_{w}^{r}) \subset Op (S_{w}^{r})$ and $S_{w}^{p} \cdot S_{w}^{q} \subset S_{w}^{r}$ , provided $1 / p + 1 / q = 1 / r$ . If instead $1 / p + 1 / q = 1 + 1 / r$ , then $S_{w}^{p} w * S_{w}^{q} \subset S_{w}^{r}$ . By modifying the definition of the $S_{w}^{p}$ -spaces, one also obtains symbol classes related to the $S (m, g)$ spaces.

Sufficient conditions for boundedness of convolution operators in rearrangement-invariant spaces.

Peleshenko, B.I. (2001)

Sibirskij Matematicheskij Zhurnal

Sufficient conditions for univalence of an integral operator defined by Al-Oboudi differential operator.

Bulut, Serap (2008)

Journal of Inequalities and Applications [electronic only]

Sur la transformée de Laplace de $t r e^{- A}$ considérée comme fonction de la diagonale de $A$

M. Gaudin (1978)

Annales de l'I.H.P. Physique théorique

Sur le spectre semi-classique d’un système intégrable de dimension 1 autour d’une singularité hyperbolique

Olivier Lablée (2007/2008)

Séminaire de théorie spectrale et géométrie

Dans cet article on décrit le spectre semi-classique d’un opérateur de Schrödinger sur $ℝ$ avec un potentiel type double puits. La description qu’on donne est celle du spectre autour du maximum local du potentiel. Dans la classification des singularités de l’application moment d’un système intégrable, le double puits représente le cas des singularités non-dégénérées de type hyperbolique.

Sur l'existence des solutions d'une équation intégro-différentielle

K. Zima (1973)

Annales Polonici Mathematici

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