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A Hilbert reciprocity law on 3-manifolds
Based on our homological idelic class field theory, we formulate an analogue of the Hilbert reciprocity law on a rational homology 3-sphere endowed...
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Schatten Classes and Commutator in the Two Weight Setting, I. Hilbert Transform
We characterize the Hilbert–Schmidt class membership of commutator with the Hilbert transform in the two weight setting. The characterization depends...
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Hilbert Spaces
In this chapter, we briefly introduce basic concepts and theorems in vector space, normed space, Banach space, and Hilbert space that are essential...
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Hilbert Spaces
Hilbert spaces form a special class of Banach spaces with the geometric notion of orthogonality of vectors, or more generally, the notion of an angle...
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Pseudo-Differential Operators of Homogeneous Symbol Class Associated with the Weinstein Transform
In this paper, pseudo-differential operators with homogeneous symbol classes associated with the Weinstein transform are introduced. The boundedness...
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Boundedness of the Hilbert Transform in Besov Spaces
Boundedness conditions are found for the Hilbert transform H in Besov spaces with Muckenhoupt weights. The operator H in this situation acts on...
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Partially defined operators on locally Hilbert spaces
We investigate partially defined operators on inductive limits of Hilbert spaces, in order to introduce an operator theory for a class of linear...
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Hilbert–Burch Linear Sections
This chapter takes an exception to the previous chapters in that the focus is on linear sections of...
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Pricing options on flow forwards by neural networks in a Hilbert space
We propose a new methodology for pricing options on flow forwards by applying infinite-dimensional neural networks. We recast the pricing problem as...
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Nonlinear Riemann-Hilbert Problems for Axial- and Bi-axial-monogenic Functions
In this paper we show a new approach to study Riemann-Hilbert (RH) problems in the context of monogenic functions over axial- and bi-axial domains....
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High-order Soliton Matrix for the Third-order Flow Equation of the Gerdjikov-Ivanov Hierarchy Through the Riemann-Hilbert Method
The Gerdjikov-Ivanov (GI) hierarchy is derived via recursion operator, in this article, we mainly investigate the third-order flow GI equation. In...
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Compositions of Random Processes in a Hilbert Space and Its Limit Distribution
AbstractRandom processes with values in an infinite dimensional linear spaces are studied. These processes are presented by the random linear...
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Regularized mean curvature flow for invariant hypersurfaces in a Hilbert space and its application to gauge theory
In this paper, we investigate a regularized mean curvature flow starting from an invariant hypersurface in a Hilbert space equipped with an isometric...
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Riemann–Hilbert Approach and N-Soliton Solutions for a Higher-Order Coupled Nonlinear Schrödinger System
In this paper, the main work is to study the N -soliton solutions for a higher-order coupled nonlinear Schrödinger system by using the method of...
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New Hilbert Space Tools for Analysis of Graph Laplacians and Markov Processes
The main objective of this paper is to develop the concepts and ideas used in the theory of weighted networks on infinite graphs. Our basic...
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On the Convergence for Randomly Weighted Sums of Hilbert-valued Coordinatewise Pairwise NQD Random Variables
In this paper, we present the complete convergence for weighted sums of coordinatewise pairwise negative quadrant dependent random variables taking...
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Controlled g-frames and dual g-frames in Hilbert spaces
As generalizations of g-frames and controlled frames, the theory of controlled g-frames has been deeply studied. This paper addresses the controlled...