The Journal of the Indian Mathematical Society

M. V. Subba Rao ¹

Affiliations
1 S. V. University, Tirupati, IN

Abstract

Let N_i(x) be a sequence of norms defined over a vector space E. Let us consider all those linear topologies T over E which are weaker than N_i(x) for all i. (For brevity N_i(x) is used to denote the norm as well as the corresponding topology). These include the lattice product tolopogy [3] of the N_i(x), i.e. the strongest topology weaker than each of the N_i(x) topologies.

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M. V. Subba Rao ¹

Affiliations
1 S. V. University, Tirupati, IN

Abstract

The object of this paper is to show that a theorem on linear continuous transformations on the space of integral functions proved by V. Ganapathy Iyer [1] holds substantially for general normed vector spaces, and to obtain an extension of the result for transformations from a directed family topologies directed by the relation "weaker than" defined on a vector space E to a family of locally bounded topologies defined over another vector space V.

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M. V. Subba Rao ¹

Affiliations
1 Presidency College, Madras, IN

Abstract

This paper arose out of a study of Ramanujan's trigonometrical sum C_m(n) defined by[4]

C_m(n)=Σ Σ^λn              (1)

where ρ=e^2πi/m and λ runs though a complete system of representatives of the prime residue classes mod m.

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M. V. Subba Rao ¹

Affiliations
1 University of Madras, IN

Abstract

The Legendre polynomial P_n(x) = I/2ⁿn dⁿ/dxⁿ (x²-I)ⁿ was generalized by Nicolas Cioranescu and Kesava Menon.

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