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On the convergence of numerical integration as a finite matrix approximation to multiplication operator
We study the convergence of a family of numerical integration methods where the numerical integration is formulated as a finite matrix approximation...
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Noncommutative Integration and Operator Theory
The purpose of this monograph is to provide a systematic account of the theory of noncommutative integration in semi-finite von Neumann algebras. It...
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Product integration rules by the constrained mock-Chebyshev least squares operator
In this paper we consider the problem of the approximation of definite integrals on finite intervals for integrand functions showing some kind of...
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Randomised one-step time integration methods for deterministic operator differential equations
Uncertainty quantification plays an important role in problems that involve inferring a parameter of an initial value problem from observations of...
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Reconstruction of the Cauchy–Riemann Operator by Complex Integration Operators along Circles
AbstractOne well-known integral condition for a function to be holomorphic is the following classical Morera theorem: if a function
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Coordinate-Adaptive Integration of PDEs on Tensor Manifolds
We introduce a new tensor integration method for time-dependent partial differential equations (PDEs) that controls the tensor rank of the PDE...
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Operator Splitting
In mathematics, a common approach to solving a new problem is to break down the problem into sub-problems that you know how to solve and then try to...
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On Boundedness of Fractional Hadamard Integration and Hadamard-Type Integration in Lebesgue Spaces with Mixed Norm
In this paper, we consider the boundedness of integrals of fractional Hadamard integration and Hadamard-type integration (mixed and directional) in...
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Some properties of the integration operators on the spaces F(p, q, s)
We study the closed range property and the strict singularity of integration operators acting on the spaces F ( p, pα − 2, s ). We completely...
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The Generalized Volterra Integral Operator and Toeplitz Operator on Weighted Bergman Spaces
We study the boundedness and compactness of the generalized Volterra integral operator on weighted Bergman spaces with doubling weights on the unit...
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A Hilbert-Schmidt integral operator and the Weil distribution
In this paper, a positive operator is given. It is shown that the product of this positive operator and the convolution operator is a trace class...
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Equiconvergence Theorem for Integral Operator on a Graph with Cycle
AbstractThe paper deals with integral operators on the simplest geometric two-edge graph containing a cycle. The class of integral operators with...
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Eigenvalue estimates for a generalized Paneitz operator
In this paper, we give some universal inequalities for the eigenvalues of a generalized Paneitz operator on a bounded domain in a complete Riemannian...
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Operator Theory
This section provides a very brief and quick review of the basics of Hilbert space theory and functional analysis that are needed for this text. We...
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Connes Integration Formula: A Constructive Approach
AbstractA version of Connes Integration Formula which provides concrete asymptotics of eigenvalues is given. This radically extends the class of...
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Wave Operator on Compact Manifolds
On an n -dimensional ( n ≥ 2) compact connected manifold without boundary, we obtain the sharp range of p to ensure the L p convergence of the wave...