Vol. 8 No. 1 (2016)
Published:
2016-02-18
Articles
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Articles
On Nagy-Foias Characteristic Function in Extensions Theory of Hermitian Operators
AbstractFor a densely defined in a Hilbert space closed Hermitian operator with infinite defect numbers its maximal extensions are discussed. The Nagy-Foias characteristic function of an arbitrary maximal dissipative extension is derived. Mutually complementary classes of such extensions, referred to as inherited and acquired are introduced, and the peculiarity of characteristic function, as determining the class of extensions it corresponds to, is noted. In the setting of Calkin's abstract boundary conditions theory abstract analogs of Nagy-Foias and Weyl functions are presented in similar manner, as operator functions involved in boundary operators, describing the class of inherited extensions. Existence and analyticity of these functions are proved.
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Articles
New inequalities of Gr\"{u}ss--Lupa\c{s} type and Applications for Selfadjoint Operators
AbstractIn this paper, some \v{C}eby\v{s}ev--Lupa\c{s} type inequalities are proved. New inequalities of Gr\"{u}ss type for Riemann--Stieltjes integral are also obtained. Applications for functions of selfadjoint operators on complex Hilbert spaces are provided as well.
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Articles
$n$-Points Inequalities of Hermite-Hadamard Type for $h$-Convex Functions on Linear Spaces
AbstractSome $n$-points inequalities of Hermite-Hadamard type for $h$-convex functions defined on convex subsets in real or complex linear spaces are given. Applications for norm inequalities are provided as well.
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Articles
Global well-posedness for the 3D Newton-Boussinesq equations
AbstractIn this paper, we prove the global well-posedness for the Newton-Boussinesq equations in $\mathbb R^3$. By fully using the Fourier localization technique, we obtain the existence and uniqueness of smooth solutions in Hilbert spaces.
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Articles
On the finite Loop Algebra of the smallest Moufang loop $M(S_3,2)$
AbstractLet $F[L]$ be a loop algebra of a loop $L$ over a field $F$. In this paper, we obtain the unit loop of the loop algebra $F[L],$ where $L$ is the smallest Moufang loop $M(S_3,2)$ and $F$ is a finite field of characteristic different from $3$.
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Articles
Frechet Lie Algebroids and Their Cohomology
AbstractWe define Lie and Courant algebroids on Frechet manifolds. Moreover, we construct a Dirac structure on the generalized tangent bundle of a Frechet manifold and show that it inherits a Frechet Lie algebroid structure. We show that the Lie algebroid cohomology of the $\mathcal{B}$-cotangent bundle Lie algebroid of a weakly symplectic Frechet manifold $M$ is the Lichnerowicz-Poisson cohomology of $M$.
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