In this paper, we prove that in a hyperconvex domain Ω in H^(n), if a non-negative Borel measure is dominated by a quaternionic Monge–Ampère measure, then it is a quaternionic Monge–Ampère measure of a fu...In this paper, we prove that in a hyperconvex domain Ω in H^(n), if a non-negative Borel measure is dominated by a quaternionic Monge–Ampère measure, then it is a quaternionic Monge–Ampère measure of a function in the class E(Ω).展开更多
We study the relations between the quaternion H-type group and the boundary of the unit ball on the two-dimensional quaternionic space.The orthogonal projection of the space of square integrable functions defined on q...We study the relations between the quaternion H-type group and the boundary of the unit ball on the two-dimensional quaternionic space.The orthogonal projection of the space of square integrable functions defined on quaternion H-type group into its subspace of boundary values of q- holomorphic functions is considered.The precise form of Cauchy-Szeg(?)kernel and the orthogonal projection operator is obtained.The fundamental solution for the operatorΔ_λis found.展开更多
Some curvature pinching theorems for compact or complete totally real minimal submanifolds in a quaternion projective space are given,so that the corresponding results due to B. Y.Chen and C. S. Houh as well as Y. B. ...Some curvature pinching theorems for compact or complete totally real minimal submanifolds in a quaternion projective space are given,so that the corresponding results due to B. Y.Chen and C. S. Houh as well as Y. B. Shen are improved and generalized.展开更多
Blind deblurring for color images has long been a challenging computer vision task.The intrinsic color structures within image channels have typically been disregarded in many excellent works.We investigate employing ...Blind deblurring for color images has long been a challenging computer vision task.The intrinsic color structures within image channels have typically been disregarded in many excellent works.We investigate employing regularizations in the hue,saturation,and value(HSV)color space via the quaternion framework in order to better retain the internal relationship among the multiple channels and reduce color distortions and color artifacts.We observe that a geometric spatial-feature prior utilized in the intermediate latent image successfully enhances the kernel accuracy for the blind deblurring variational models,preserving the salient edges while decreasing the unfavorable structures.Motivated by this,we develop a saturation-value geometric spatial-feature prior in the HSV color space via the quaternion framework for blind color image deblurring,which facilitates blur kernel estimation.An alternating optimization strategy combined with a primal-dual projected gradient method can effectively solve this novel proposed model.Extensive experimental results show that our model outperforms state-of-the-art methods in blind color image deblurring by a wide margin,demonstrating the effectiveness of the proposed model.展开更多
A norm of a quaternion matrix is defined. The expressions of the least square solutions of the quaternion matrix equation AX = B and the equation with the constraint condition DX = E are given.
In this paper we derive a practical method of solving simultaneously the problem of Schmidt decomposition of quaternion matrix and the orthonormalization of vectors in a generalized unitary space by using elementary c...In this paper we derive a practical method of solving simultaneously the problem of Schmidt decomposition of quaternion matrix and the orthonormalization of vectors in a generalized unitary space by using elementary column operations on matrices over the quaternion field.展开更多
The aim of this paper is to prove a new version of the Riesz-Thorin interpolation theorem on L^(P)(C,H).In the sense of Cullen-regular,we show Hadamard’s three-lines theorem by means of the Maximum modulus principle ...The aim of this paper is to prove a new version of the Riesz-Thorin interpolation theorem on L^(P)(C,H).In the sense of Cullen-regular,we show Hadamard’s three-lines theorem by means of the Maximum modulus principle on a symmetric slice domain.In addition,two applications of the Riesz-Thorin theorem are presented.Finally,we investigate two kinds of Calderón’s complex interpolation methods in LP(C,H).展开更多
文摘In this paper, we prove that in a hyperconvex domain Ω in H^(n), if a non-negative Borel measure is dominated by a quaternionic Monge–Ampère measure, then it is a quaternionic Monge–Ampère measure of a function in the class E(Ω).
基金The first author is partially supported by a Competitive Research Grant at Georgetown University(Grant No.GD2236120)The second author is partially supported by grants of the Norwegian Council(Grant Nos.177355/V30,180275/D15)by the grant of the European Science Foundation Networking Programme HCAA.
文摘We study the relations between the quaternion H-type group and the boundary of the unit ball on the two-dimensional quaternionic space.The orthogonal projection of the space of square integrable functions defined on quaternion H-type group into its subspace of boundary values of q- holomorphic functions is considered.The precise form of Cauchy-Szeg(?)kernel and the orthogonal projection operator is obtained.The fundamental solution for the operatorΔ_λis found.
文摘Some curvature pinching theorems for compact or complete totally real minimal submanifolds in a quaternion projective space are given,so that the corresponding results due to B. Y.Chen and C. S. Houh as well as Y. B. Shen are improved and generalized.
基金the National Key R&D Program of China under Grant 2021YFE0203700Grant NSFC/RGC N CUHK 415/19,Grant ITF MHP/038/20,Grant CRF 8730063Grant RGC 14300219,14302920,14301121,CUHK Direct Grant for Research.
文摘Blind deblurring for color images has long been a challenging computer vision task.The intrinsic color structures within image channels have typically been disregarded in many excellent works.We investigate employing regularizations in the hue,saturation,and value(HSV)color space via the quaternion framework in order to better retain the internal relationship among the multiple channels and reduce color distortions and color artifacts.We observe that a geometric spatial-feature prior utilized in the intermediate latent image successfully enhances the kernel accuracy for the blind deblurring variational models,preserving the salient edges while decreasing the unfavorable structures.Motivated by this,we develop a saturation-value geometric spatial-feature prior in the HSV color space via the quaternion framework for blind color image deblurring,which facilitates blur kernel estimation.An alternating optimization strategy combined with a primal-dual projected gradient method can effectively solve this novel proposed model.Extensive experimental results show that our model outperforms state-of-the-art methods in blind color image deblurring by a wide margin,demonstrating the effectiveness of the proposed model.
文摘A norm of a quaternion matrix is defined. The expressions of the least square solutions of the quaternion matrix equation AX = B and the equation with the constraint condition DX = E are given.
文摘In this paper we derive a practical method of solving simultaneously the problem of Schmidt decomposition of quaternion matrix and the orthonormalization of vectors in a generalized unitary space by using elementary column operations on matrices over the quaternion field.
基金supported by the Innovation Research for the Postgrad-uates of Guangzhou University(2020GDJC-D06)supported by the National Natural Science Foundation of China(12071229)。
文摘The aim of this paper is to prove a new version of the Riesz-Thorin interpolation theorem on L^(P)(C,H).In the sense of Cullen-regular,we show Hadamard’s three-lines theorem by means of the Maximum modulus principle on a symmetric slice domain.In addition,two applications of the Riesz-Thorin theorem are presented.Finally,we investigate two kinds of Calderón’s complex interpolation methods in LP(C,H).