The classical theory of Gaussian quadrature assumes a positive weight function. We will show that in some cases Gaussian rules can be constructed with respect to an oscillatory weight, yielding methods with complex quadrature nodes and positive weights. These rules are well suited for highly oscillatory integrals because they attain optimal asymptotic order. We show that for the Fourier oscilla...

Tonewood for musical instruments is quarter-sawn and frequently quality-graded based on visual appearance, mechanical and acoustic properties. The assessment uses simple human (subjective) observation, and two ‘‘experts’’ can rate the same sample differently. This paper describes the application of integral transforms (Fourier and Radon) for automatic (objective) assessment of the visual appear...

We survey a family of theories that enable to process polar data via integral transforms. We show the relation between irregular sampling and discrete integral transforms, demonstrate the application of irregular (polar) sampling to image processing problems, and derive approximation algorithms that are based on unequally spaced samples. It is based on sampling the Fourier domain. We describe 2...

For some general linear integral operator equations, we investigate consequent initial value problems by using the theory of reproducing kernels. A new method is proposed which – in particular – generates a new field among initial value problems, linear integral operators, eigenfunctions and values, integral transforms and reproducing kernels. In particular, examples are worked out for the inte...

Integral transforms provide us great convenience in finding exact and approximate solutions of many mathematical physics engineering problems such as signals, wave equation, heat conduction, transfer. In this study, we consider the Kashuri Fundo transform, which is one these integral transforms, our aim to show that transform an effective method solving steady transfer obtained results are comp...