Dosi, Anar
In the present paper we introduce quantum measures as a concept of quantum functional analysis and develop the fractional space technique in the quantum (or local operator) space framework. We prove that each local operator algebra (or quantum *-algebra) has a fractional space realization. This approach allows us to formulate and prove a noncommutative Albrecht-Vasilescu extension theorem, which in turn solves the quantum moment problem.


Exponential type complex and non-Hermitian potentials within quantum Hamilton-Jacobi formalism
Yesiltas, Oezlem; Sever, Ramazan (Springer Science and Business Media LLC, 2008-03-01)
PT-/non-PT-symmetric and non-Hermitian deformed Morse and Poschl-Teller potentials are studied first time by quantum Hamilton-Jacobi approach. Energy eigenvalues and eigenfunctions are obtained by solving quantum Hamilton-Jacobi equation.
Hyperbolic conservation laws on manifolds. An error estimate for finite volume schemes
Lefloch, Philippe G.; Okutmuştur, Baver; Neves, Wladimir (Springer Science and Business Media LLC, 2009-07-01)
Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Riemannian manifold, and we establish an L (1)-error estimate for a class of finite volume schemes allowing for the approximation of entropy solutions to the initial value problem. The error in the L (1) norm is of order h (1/4) at most, where h represents the maximal diameter of elements in the family of geodesic triangulations. The proof relies on a suitable generalization of Cockburn, Coquel, and LeFloch's theo...
Intelligent analysis of chaos roughness in regularity of walk for a two legged robot
Kaygisiz, BH; Erkmen, İsmet; Erkmen, Aydan Müşerref (Elsevier BV, 2006-07-01)
We describe in this paper a new approach to the identification of the chaotic boundaries of regular (periodic and quasiperiodic) regions in nonlinear systems, using cell mapping equipped with measures of fractal dimension and rough sets. The proposed fractal-rough set approach considers a state space divided into cells where cell trajectories are determined using cell to cell mapping technique. All image cells in the state space, equipped with their individual fractal dimension are then classified as being ...
Strictly singular operators and isomorphisms of Cartesian products of power series spaces
Djakov, PB; Onal, S; Terzioglu, T; Yurdakul, Murat Hayrettin (1998-01-02)
V. P. Zahariuta, in 1973, used the theory of Fredholm operators to develop a method to classify Cartesian products of locally convex spaces. In this work we modify his method to study the isomorphic classification of Cartesian products of the kind E-0(p)(a) x E-infinity(q) (b) where 1 less than or equal to p, q < infinity, p not equal q, a = (a(n))(n=1)(infinity) and b = (b(n))(n=1)(infinity) are sequences of positive numbers and E-0(p)(a), E(infinity)q(b) are respectively l(p)-finite and l(q)-infinite type...
Shape-invariance approach and Hamiltonian hierarchy method on the Woods-Saxon potential for l not equal 0 states
Berkdemir, Cueneyt; BERKDEMİR, Ayşe; Sever, Ramazan (Springer Science and Business Media LLC, 2008-03-01)
An analytically solvable Woods-Saxon potential for l not equal 0 states is presented within the framework of Supersymmetric Quantum Mechanics formalism. The shape-invariance approach and Hamiltonian hierarchy method are included in calculations by means of a translation of parameters. The approximate energy spectrum of this potential is obtained for l not equal 0 states, applying the Woods-Saxon square approximation to the centrifugal barrier term of the Schrodinger equation.
Citation Formats
A. Dosi, “LOCAL OPERATOR ALGEBRAS FRACTIONAL POSITIVITY AND THE QUANTUM MOMENT PROBLEM,” TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, pp. 801–856, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63574.