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Currently displaying 1 – 3 of 3

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An extension of a theorem of Marcinkiewicz and Zygmund on differentiability

S. Mukhopadhyay; S. Mitra — 1996

Fundamenta Mathematicae

Let f be a measurable function such that $Δ_{k} (x, h; f) = {O (| h |}^{λ})$ at each point x of a set E, where k is a positive integer, λ > 0 and $Δ_{k} (x, h; f)$ is the symmetric difference of f at x of order k. Marcinkiewicz and Zygmund [5] proved that if λ = k and if E is measurable then the Peano derivative $f_{(k)}$ exists a.e. on E. Here we prove that if λ > k-1 then the Peano derivative $f_{([λ])}$ exists a.e. on E and that the result is false if λ = k-1; it is further proved that if λ is any positive integer and if the approximate Peano derivative...

On certain new connections between. Legendre and Bessel Functions

S. C. Mitra — 1936

Mathematische Zeitschrift

On parabolic cylinder functions which are self - reciprocal in the Hankel-transform

Dr. S. C., Dacca, Bengal (Brit Mitra — 1938

Mathematische Zeitschrift

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