Conjugate Jacobi Series and Conjugate Functions

Combination of Jacobi - Davidson and Conjugate Gradients

A Note on Conjugate Functions

1. Statement of results. The purpose of this note is to discuss as simply as possible a generalization of the classical theorem of M. Riesz2 on the integrability of the conjugate functions of functions in LP, and to point out some of the consequences for Fourier series. Suppose that(t) is a non-negative, convex function defined for t^O with (2t) ̂K<p(t) ior some constant K. Th...

Monotone operators and “bigger conjugate” functions

We study a question posed by Stephen Simons in his 2008 monograph involving “bigger conjugate” (BC) functions and the partial infimal convolution. As Simons demonstrated in his monograph, these function have been crucial to the understanding and advancement of the state-of-the-art of harder problems in monotone operator theory, especially the sum problem. In this paper, we provide some tools fo...

Conjugate Harmonic Functions and Clifford Algebras

We generalize a Hardy-Littlewood inequality and a Privalov inequality for conjugate harmonic functions in the plane to components of Clifford-valued monogenic functions.

Generalized Conjugate and Analytic Functions without Expansions.

On a Lebesgue measure space with measure element do, and total measure finite or infinite, we consider the complex-valued measurable functions f, y, so, ., each determined only a.e., and each belonging to all L,-classes simultaneously, 1<r< a. We donote (i) by F = {f} a ring of functions with complex constants and ordinary multiplication and closed under the involution: if f -= f + if2 e F then...