QUADRATIC INTEGRABILITY AND BOUNDEDNESS OF THE SOLUTIONS FOR SECOND ORDER NONLINEAR DELAY DIFFERENTIAL EQUATIONS

In this paper, by means of auxiliary functions and inequalities, we obtain some sufficient conditions of second order nonhomogeneous delay differential equation belonging to the L.S. or L.S. ∩L.C..     

NEW WAVELET BASES FOR NON－HOMOGENEOUS SYMBOLIC SPACE OpS1,1^m AND RELATED KERNEL－DISTRIBUTION SPACES

This paper constructs several classes of new wavelet bases, which are unconditional bases for related operator spaces. Using these bases, the author analyzes non-homogeneous symbolic space OpSm1,1 and two related kernel-distribution spaces, and characterizes them in two wavelet coefficients spaces. Besides, some properties for singular integral operators are studied.     

THE TRACE SPACE INVARIANT AND UNITARY GROUP OF C^＊—ALGEBRA

Let A be a unital C-algebra, n ∈ N ∪ {∞}. It is proved that the isomorphism △n : is isometric for some suitable distances. Asan application, the author has the split exact sequence with iA contractive (and isometric if n = ∞) under certain condition of A.