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On maximal function of discrete rough truncated Hilbert transforms
We prove the weak type (1,1) estimate for maximal function of the truncated rough Hilbert transform considered in Paluszy’nski (ASNSCS 910:679-704,...
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Five Hilbert Space Models Related to the Riemann Zeta Function
In a recent work of the author, a de Branges space was constructed, as well as an operator on it whose spectrum coincides with the set of nontrivial...
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Hilbert Functions
In this chapter, we will describe some connections among the Hilbert functions of X,...
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Hilbert Spaces
Inner products are generalizations of the dot product in $$\mathbb...
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A half-discrete Hilbert-type inequality in the whole plane with the constant factor related to a cotangent function
In this work, by the introduction of some parameters, a new half-discrete kernel function in the whole plane is defined, which involves both the...
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On minimal Gorenstein Hilbert functions
We conjecture that a class of Artinian Gorenstein Hilbert algebras called full Perazzo algebras always have minimal Hilbert function, fixing...
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Hilbert Spaces
A Hilbert space is a special kind of Banach space, where the norm is induced by the inner product. All of the results for Banach spaces are valid in...
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Hilbert Spaces
Hilbert spaces form a special class of Banach spaces with the geometric notion of orthogonality of vectors, or more generally, the notion of an angle...
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Hilbert Spaces
In this chapter, we briefly introduce basic concepts and theorems in vector space, normed space, Banach space, and Hilbert space that are essential...
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Hilbert Spaces
TheHilbert theory of Hilbert spacesHilbert space is a fundamental area of analysis and has wide applications to partial differential equations and...
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Hilbert Spaces
Let H be a complex linear space. A function $$(\cdot ,\cdot ):H\times...
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On a more accurate half-discrete multidimensional Hilbert-type inequality involving one derivative function of m-order
By means of the weight functions, the idea of introduced parameters, using the transfer formula and Hermite–Hadamard’s inequality, a more accurate...
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Hilbert spaces
The goal of this chapter is to give an elementary but comprehensive introduction to the theory of Hilbert spaces, where we wish to highlight the...
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A new reverse Hardy–Hilbert inequality with the power function as intermediate variables
In this paper, by virtue of the symmetry principle, applying the techniques of real analysis and Euler–Maclaurin summation formula, we construct...
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Hilbert Transform in the Cartwright–de Branges Space
Contrary to celebrated transforms such as the Fourier transform, explicit formulas for the Hilbert transform of well-known functions are rare. In...
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Riemann–Hilbert problems
The various Riemann-Hilbert problems involve constructing of holomorphic functions subject to certain relations. This has connections to the...