scholarly journals Embedding of Qp spaces into tent spaces and Volterra integral operator

2021 ◽  
Vol 6 (1) ◽  
pp. 698-711
Author(s):  
Ruishen Qian ◽  
◽  
Xiangling Zhu ◽  
Keyword(s):  
Integral Operator ◽  
Tent Spaces ◽  
Volterra Integral Operator

scholarly journals Embedding of Besov Spaces and the Volterra Integral Operator

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Dan Qu ◽  
Xiangling Zhu ◽  
Ruishen Qian
Keyword(s):  
Integral Operator ◽  
Besov Spaces ◽  
Essential Norm ◽  
Function Spaces ◽  
General Function ◽  
Tent Spaces ◽  
Volterra Integral Operator ◽  
Inclusion Mapping

The boundedness and compactness of the inclusion mapping from Besov spaces to tent spaces are studied in this paper. Meanwhile, the boundedness, compactness, and essential norm of the Volterra integral operator T g from Besov spaces to a class of general function spaces are also investigated.

scholarly journals Nonlinear Evolution Equations with Exponentially Decaying Memory: Existence via Time Discretisation, Uniqueness, and Stability

2020 ◽  
Vol 20 (1) ◽  
pp. 89-108 ◽  
Author(s):  
André Eikmeier ◽  
Etienne Emmrich ◽  
Hans-Christian Kreusler
Keyword(s):  
Banach Space ◽  
Integral Operator ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Inner Product ◽  
Initial Value ◽  
Time Discretisation ◽  
Volterra Integral Operator ◽  
Stability Results

AbstractThe initial value problem for an evolution equation of type {v^{\prime}+Av+BKv=f} is studied, where {A:V_{A}\to V_{A}^{\prime}} is a monotone, coercive operator and where {B:V_{B}\to V_{B}^{\prime}} induces an inner product. The Banach space {V_{A}} is not required to be embedded in {V_{B}} or vice versa. The operator K incorporates a Volterra integral operator in time of convolution type with an exponentially decaying kernel. Existence of a global-in-time solution is shown by proving convergence of a suitable time discretisation. Moreover, uniqueness as well as stability results are proved. Appropriate integration-by-parts formulae are a key ingredient for the analysis.

Inverse nodal problems for integro-differential operators with a constant delay

2019 ◽  
Vol 27 (4) ◽  
pp. 501-509 ◽  
Author(s):  
Murat Sat ◽  
Chung Tsun Shieh
Keyword(s):  
Integral Operator ◽  
Potential Function ◽  
Liouville Operator ◽  
Differential Operators ◽  
Constant Delay ◽  
Nodal Points ◽  
Inverse Nodal Problems ◽  
Volterra Integral Operator ◽  
Sturm Liouville

Abstract We study inverse nodal problems for Sturm–Liouville operator perturbed by a Volterra integral operator with a constant delay. We have estimated nodal points and nodal lengths for this operator. Moreover, by using these data, we have shown that the potential function of this operator can be established uniquely.

scholarly journals Norm of a Volterra Integral Operator on Some Analytic Function Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Hao Li ◽  
Songxiao Li
Keyword(s):  
Analytic Function ◽  
Integral Operator ◽  
Unit Disc ◽  
Function Spaces ◽  
Volterra Integral Operator ◽  
Analytic Function Spaces

Let f be an analytic function in the unit disc 𝔻. The Volterra integral operator If is defined as follows: If(h)(z)=∫0zf(w)h'(w)dw,h∈H(𝔻),z∈𝔻. In this paper, we compute the norm of If on some analytic function spaces.

Volterra integral operator and essential norm on Dirichlet type spaces

2021 ◽  
Vol 6 (9) ◽  
pp. 10092-10104
Author(s):  
Liu Yang ◽  
◽  
Ruishen Qian ◽  
Keyword(s):  
Integral Operator ◽  
Essential Norm ◽  
Dirichlet Type ◽  
Type Spaces ◽  
Volterra Integral Operator ◽  
Dirichlet Type Spaces

The exponential characteristic of the Volterra integral operator with kernel depending on 2N variables

2007 ◽  
Vol 147 (1) ◽  
pp. 6458-6463
Author(s):  
O. A. Mudrakova ◽  
L. K. Orlik
Keyword(s):  
Integral Operator ◽  
Volterra Integral Operator

Spectrum of Volterra integral operator of the second kind

2016 ◽  
Author(s):  
Meiramkul Amangaliyeva ◽  
Muvasharkhan Jenaliyev ◽  
Madi Ergaliev ◽  
Murat Ramazanov
Keyword(s):  
Integral Operator ◽  
Volterra Integral Operator

An Eigenvalue Problem for a Volterra Integral Operator with Infinite Delay

1985 ◽  
Vol 16 (3) ◽  
pp. 541-547
Author(s):  
Gustaf Gripenberg
Keyword(s):  
Integral Operator ◽  
Eigenvalue Problem ◽  
Infinite Delay ◽  
Volterra Integral Operator
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