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We deal with several classes of integral transformations of the form
where is an operator. In case is the identity operator, we obtain several operator properties on with weights for a generalized operator related to the Fourier cosine and the Kontorovich-Lebedev integral transforms. For a class of differential operators of infinite order, we prove the unitary property of these transforms on and define the inversion formula. Further, for an other class of differential operators of finite...
Inspired by work of Montgomery on Fourier series and Donoho-Strak in signal processing, we investigate two families of rearrangement inequalities for the Fourier transform. More precisely, we show that the behavior of a Fourier transform of a function over a small set is controlled by the behavior of the Fourier transform of its symmetric decreasing rearrangement. In the case, the same is true if we further assume that the function has a support of finite measure.As a byproduct, we also give...
Using the theory of Newton Polygons, we formulate a simple criterion for the Galois group of a polynomial to be “large.” For a fixed , Filaseta and Lam have shown that the th degree Generalized Laguerre Polynomial is irreducible for all large enough . We use our criterion to show that, under these conditions, the Galois group of is either the alternating or symmetric group on letters, generalizing results of Schur for .
Mathematics Subject Classification: 33C60, 33C20, 44A15This paper is devoted to an important case of Wright’s hypergeometric function 2Fτ,β1(a, b; c; z) = 2Fτ,β1(z), to studying its basic properties and to application of 2Fτ,β1(z) to the generalization of the associated Legendre functions.
2000 Mathematics Subject Classification: 26A33, 33C20This paper is devoted to further development of important case of
Wright’s hypergeometric function and its applications to the generalization
of Γ-, B-, ψ-, ζ-, Volterra functions.
The incomplete Gamma function and its associated functions and are defined as locally summable functions on the real line and some convolutions and neutrix convolutions of these functions and the functions and are then found.
The main objective of this paper is to give the specific forms of the meromorphic solutions of the nonlinear difference-differential equation
where is a difference-differential polynomial in of degree with small functions of as its coefficients, , are nonzero rational functions and , are non-constant polynomials. More precisely, we find out the conditions for ensuring the existence of meromorphic solutions of the above equation.
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