Herz-Type Hardy Spaces for the Dunkl Operator on the Real Line

2000 Mathematics Subject Classification: Primary 46F12, Secondary 44A15, 44A35

An Analogue of Beurling-Hörmander’s Theorem for the Dunkl-Bessel Transform

Mathematics Subject Classification: Primary 35R10, Secondary 44A15

Perturbed Proximal Point Algorithm with Nonquadratic Kernel

Let H be a real Hilbert space and T be a maximal monotone operator on H. A well-known algorithm, developed by R. T. Rockafellar [16], for solving the problem (P) ”To find x ∈ H such that 0 ∈ T x” is the proximal point algorithm. Several generalizations have been considered by several authors: introduction of a perturbation, introduction of a variable metric in the perturbed algorithm, introduction of a pseudo-metric in place of the classical regularization, . . . We summarize some of these extensions by taking simultaneously into account a pseudo-metric as regularization and a perturbation in an inexact version of the algorithm.

On the Relationships Among Quantified Autoepistemic Logic, its Kernel, and Quantified Reflective Logic

A Quantified Autoepistemic Logic is axiomatized in a monotonic Modal Quantificational Logic whose modal laws are slightly stronger than S5. This Quantified Autoepistemic Logic obeys all the laws of First Order Logic and its L predicate obeys the laws of S5 Modal Logic in every fixed-point. It is proven that this Logic has a kernel not containing L such that L holds for a sentence if and only if that sentence is in the kernel. This result is important because it shows that L is superfluous thereby allowing the ori ginal equivalence to be simplified by eliminating L from it. It is also shown that the Kernel of Quantified Autoepistemic Logic is a generalization of Quantified Reflective Logic, which coincides with it in the propositional case.

An Abstract Second Kind Fredholm Integral Equation with Degenerated Kernel

Mathematics Subject Classification: 44A40, 45B05

On the Uniform Convergence of Partial Dunkl Integrals in Besov-Dunkl Spaces

2000 Mathematics Subject Classification: 44A15, 44A35, 46E30

Commutants of the Dunkl Operators in C(R)

2000 Mathematics Subject Classification: 44A35; 42A75; 47A16, 47L10, 47L80

Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R

2000 Mathematics Subject Classification: 34K99, 44A15, 44A35, 42A75, 42A63

Generalized Sobolev Spaces of Exponential Type Associated with the Dunkl Operators

2000 Mathematics Subject Classification: 35E45

Spectrum of Functions for the Dunkl Transform on R^d

Mathematics Subject Classification: 42B10

Representations of Inverse Functions by the Integral Transform with the Sign Kernel

Mathematics Subject Classification: Primary 30C40

On the Range and the Kernel of Derivations

2000 Mathematics Subject Classification: Primary 47B47, 47B10; Secondary 47A30.

Large and Moderate Deviations Principles for Recursive Kernel Estimator of a Multivariate Density and its Partial Derivatives

2000 Mathematics Subject Classification: 62G07, 60F10.

Dispersion Phenomena in Dunkl-Schrödinger Equation and Applications

2000 Mathematics Subject Classification: 35Q55,42B10.

Dunkl-Schrödinger Equations with and without Quadratic Potentials

2000 Mathematics Subject Classification: Primary 42A38. Secondary 42B10.