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Chandrasekharan, K.
- A Note on Typical Means
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1 Tata Institute of Fundamental Research, Bombay, IN
2 Andhra University, Waltair, IN
1 Tata Institute of Fundamental Research, Bombay, IN
2 Andhra University, Waltair, IN
Source
The Journal of the Indian Mathematical Society, Vol 18, No 1 (1954), Pagination: 107-114Abstract
This note has for its object the clarification of certain points in our book [1]. This clarification seems to us to be necessary in order to remove possible misconceptions regarding the validity of some of the results in [I] which are discussed in [2]; it will appear that those results are correct. We take this opportunity also to touch on some points other than those arising from [2], Chapter and page references, unless otherwise indioated, apply to the book.- The Absolute Summability of Series of Eigenfunctions
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1 Madras University, IN
1 Madras University, IN
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The Journal of the Indian Mathematical Society, Vol 7 (1943), Pagination: 25-30Abstract
The problem of summability of series of eigenfunctions of boundary-value problems has been solved by Dr. S. Minakshisundaram, by making use of the method of Bessel-summability developed by me in a paper which is not yet published. The object of this note is to answer the corresponding question of absolute summability.- Bessel-Summability of the Product of Two Series
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1 University of Madras, IN
1 University of Madras, IN
Source
The Journal of the Indian Mathematical Society, Vol 7 (1943), Pagination: 31-35Abstract
The method of Bessel summation of series which was developed by me in a previous paper is applied here to study the summability of the product of two given series. This product, however, is not the well-known Cauchy-product; I call it the Bessel-product.- The Second Theorem of Consistency for Absolutely Summable Series
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1 University of Madras, IN
1 University of Madras, IN
Source
The Journal of the Indian Mathematical Society, Vol 6 (1942), Pagination: 168-180Abstract
The Second Theorem of Consistency for summable series has been proved by Hardy in the following form: If
(i) the series Σcn is summable (λ, k) to the sum C,
(ii) μ is a logarithmico-exponential function of λ such that μ = O(λρ),
where Δ is a constant, then, the series Σcn is summable (μ, k) to the sum C.
The object of this paper is to prove the corresponding theorem for absolutely summable series.
- On Hadamard's Factorization Theorem
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1 University of Madras, IN
1 University of Madras, IN