New Bochner type theorems

Nonstandard Proofs of Herglotz, Bochner and Bochner-Minlos Theorems

We describe a unified approach to Herglotz, Bochner and BochnerMinlos theorems using a combination of Daniell integral and nonstandard analysis. The proofs suggest a natural extension of the last two theorems to the case when the characteristic function is not continuous. This extension is proven and is demonstrated to be the best one possible. The goal of this paper is to show how the classic ...

From Vanishing Theorems to Estimating Theorems: the Bochner Technique Revisited

Introduction Organization of the paper Sections A Basic Riemannian geometry B Examples of vanishing and estimating theorems C More Riemannian geometry D Proof of Theorem II E Bochner's theorem and estimating theorems in a more general setting F Proofs of the estimating theorems (sketch of) G From vanishing to estimating theorems : an account H Possible extensions of the methods I Final comments...

Quantum Bochner theorems and incompatible observables

A quantum version of Bochner’s theorem characterising Fourier transforms of probability measures on locally compact Abelian groups gives a characterisation of the Fourier transforms of Wigner quasi-joint distributions of position and momentum. An analogous quantum Bochner theorem characterises quasi-joint distributions of components of spin. In both cases quantum states in which a true distribu...

Strong Convergence Theorems for Nonexpansive Semigroups without Bochner Integrals

Fixed point theorems for new J-type mappings in modular spaces

In this paper, we introduce $rho$-altering $J$-type mappings in modular spaces. We prove some fixed point theorems for $rho$-altering and $rho$-altering $J$-type mappings in modular spaces. We also furnish illustrative examples to express relationship between these mappings. As a consequence, the results are applied to the existence of solution of an integral equation arising from an ODE ...