our aim in this paper is to prove an analog of younis's theorem on the image under the jacobi transform of a class functions satisfying a generalized dini-lipschitz condition in the space $mathrm{l}_{(alpha,beta)}^{p}(mathbb{r}^{+})$, $(1< pleq 2)$. it is a version of titchmarsh's theorem on the description of the image under the fourier transform of a class of functions satisfying the dini-lip...

In this paper the approximation of functions by linear means Fourier series in weighted variable exponent Lebesgue spaces was studied. This result applied to Faber Smirnov classes with defined on simply connected domain complex plane.

1. Provocative example 2. Natural function spaces on the circle S = R/2πZ 3. Topology on C∞(S1) 4. Pointwise convergence of Fourier series 5. Distributions: generalized functions 6. Invariant integration, periodicization 7. Hilbert space theory of Fourier series 8. Levi-Sobolev inequality, Levi-Sobolev imbedding 9. C∞(S1) = limC(S) = limH(S) 10. Distributions, generalized functions, again 11. T...

Shape is one of the primary features in Content Based Image Retrieval (CBIR). Many shape representations and retrieval methods exist. However, most of those methods either do not well capture shape features or are difficult to do normalization (or matching). Among them, methods based Fourier descriptors (FDs) achieve both good representation and easy normalization. FDs is often blamed for not b...

Can we learn a sparse graph from observing the value of a few random cuts? This and more general problems can be reduced to the challenge of learning set functions known to have sparse Fourier support contained in some collection P. We prove that if we choose O(k log |P|) sets uniformly at random, then with high probability, observing any k-sparse function on those sets is sufficient to recover...

We present some inequalities of Ostrowski and trapezoid type with complex exponential weight, for complex-valued absolutely continuous functions. These inequalities are related to Pompeiu’s mean value theorem. Special cases of these inequalities are applied to obtain (i) some approximation results for the finite Fourier and Laplace transforms; (ii) refinements of the Ostrowski and trapezoid ine...

This paper introduces the technique of Fourier analysis applied to Boolean functions. We use this technique to illustrate proofs of both Arrow’s Impossibility Theorem and H̊astad’s 3-bit Theorem.

1. Statement of the principal result. The class of sequences obtainable as Fourier coefficients of measures on the circle group presents numerous structure problems of interest. Amongst the earliest results somewhat akin to that stated below appear Banach's theorems about lacunary coefficients; see e.g., [4, pp. 215-220]. More recently Helson [3] has studied analogous questions when the group c...

Epithelial cells acquire diverse shapes relating to their different functions. This is particularly relevant for the cochlear outer hair cells (OHCs), whose apical and basolateral shapes accommodate the functioning of these cells as mechano-electrical and electromechanical transducers, respectively. We uncovered a circumferential shape transition of the apical junctional complex (AJC) of OHCs, ...