Among his topics are bases in Hilbert and Banach spaces, the
summability of series in the principle vectors of non-self-adjoint operators, ?-convergence operators, analytic operators in Bela Szokefalvi-Nagy's sense, the perturbation method for sound radiation by a vibrating plate in a light fluid, and applications to mathematical models.
In [14], Subrahmanyam defined the Cesaro
summability of sequences of fuzzy numbers and proved some related Tauberian theorems.
We remark that there are always important restrictions on the dimension n of the space, the order of "singularity" r, and the
summability exponent p (see, e.g., [23, 25-29], where different variants of Hardy or Caffarelli-Kohn-Nirenberg type inequalities are proved).
Then we complete this section with some significant results of four-dimensional matrix mapping via the dual
summability methods for double sequences which has been introduced and studied by Basar [20] and Yesilkayagil and Basar [21] and has been recently applied in [10, 12].
Schoenberg, "The integrability of certain functions and related
summability methods," The American Mathematical Monthly, vol.
Summability of formal solutions to singularly perturbed linear systems with irregular singularity at z = 0,
Nuray and Rhoades [26] extended the notion of Wijsman convergence of sequences of sets to that of Wijsman statistical convergence and introduced the notion of Wijsman strong Cesaro
summability of sequences of sets and discussed its relations with Wijsman statistical convergence.
Let us consider the 2[pi]-periodic trigonometric polynomial operator (or
summability operator)
for i = 1, ..., n, where F, G : [bar.[OMEGA]] x [R.sup.N] [right arrow] R are measurable with respect to x, for all [xi] [member of] [R.sup.N], continuously differentiable in [xi], for almost every x [member of] [bar.[OMEGA]] and satisfy the standard
summability condition
Moore, "The
summability of the developments in Bessel functions, with applications," Transactions of the American Mathematical Society, vol.
Until recently, there was a dearth of nontrivial examples for field theory models where sufficient information would be available to decide the question of Borel
summability in a definite manner.
Now, let A = [[a.sub.jn]], j,n [member of] N, be an infinite
summability matrix.