相关论文: Realizability with a Local Operator of A.M. Pitts

This work introduces a novel framework of uniform realizability that unifies and generalizes various realizability interpretations of logic, particularly focussing on the treatment of atomic formulas and quantifiers. Traditional…

In this work we treat realization results for operator-valued functions which are analytic in the complex sense or slice hyperholomorphic over the quaternions. In the complex setting, we prove a realization theorem for an operator-valued…

We show that any function can be locally approximated by solutions of prescribed linear equations of nonlocal type. In particular, we show that every function is locally $s$-caloric, up to a small error. The case of non-elliptic and…

We employ a new tool (sights) to investigate local operators in the Effective Topos. A number of new such local operators is analyzed using this machinery. Moreover, we investigate a local operator defined in the thesis of A. Pitts, and…

We consider non-local elliptic operators with kernel $K(y)=a(y)/|y|^{d+\sigma}$, where $0 < \sigma < 2$ is a constant and $a$ is a bounded measurable function. By using a purely analytic method, we prove the continuity of the non-local…

We consider a randomised version of Kleene's realisability interpretation of intuitionistic arithmetic in which computability is replaced with randomised computability with positive probability. In particular, we show that (i) the set of…

Einstein introduced the locality principle which states that all physical effect in some finite space-time region does not influence its space-like separated finite region. Recently, in algebraic quantum field theory, R\'{e}dei captured the…

The invertibility of integral linear operators is a major problem of both theoretical and practical importance. In this paper we investigate the relation between an operator invertibility and the rank of its integral kernel to develop a…

An elegant strategy for proving impossibility results in distributed computing was introduced in the celebrated FLP consensus impossibility proof. This strategy is local in nature as at each stage, one configuration of a hypothetical…

We introduce a general difference quotient representation for non-local operators associated with a first-order linear operator. We establish new local to non-local estimates and strong localization principles in various spaces of…

We introduce a notion of realizability with ordinal Turing machines based on recognizability rather than computability, i.e., the ability to uniquely identify an object. We show that the arising concept of $r$-realizabilty has the property…

In this paper we give a proof of the Nirenberg-Treves conjecture: that local solvability of principal type pseudo-differential operators is equivalent to condition ($\Psi$). This condition rules out certain sign changes of the imaginary…

In this article we consider a class of non-degenerate elliptic operators obtained by superpositioning the Laplacian and a general nonlocal operator. We study the existence-uniqueness results for Dirichlet boundary value problems, maximum…

We prove that arbitrary superharmonic functions and superparabolic functions related to the $p$-Laplace and the $p$-parabolic equations are locally obtained as limits of supersolutions with desired convergence properties of the…

In this article we introduce a new type of local zeta functions and study some connections with pseudodifferential operators in the framework of non-Archimedean fields. The new local zeta functions are defined by integrating complex powers…

For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect…

Following the ideas of Andrei Lerner in [ A pointwise estimate for the local sharp maximal function with applications to singular integrals" Bull. London Math. Soc. 42 (2010) 843856], we obtain another decomposition of an arbitrary…

We study the local solvability of a class of operators with multiple characteristics. The class considered here complements and extends the one studied in [9], in that in this paper we consider some cases of operators with complex…

For any partial combinatory algebra (PCA for short) A, the class of A-representable partial functions from N to A quotiented by the filter of cofinite sets of N, is a PCA such that the representable partial functions are exactly the…

In 1968 Tate introduced a new approach to residues on algebraic curves, based on a certain ring of operators that acts on the completion at a point of the function field of the curve. This approach was generalized to higher dimensional…