Integral of Complex-Valued Measurable Function

被引：6

作者：

Narita, Keiko

Endou, Noboru ^{[1
]}

Shidama, Yasunari ^{[2
]}

机构：

[1] Gifu Natl Coll Technol, Motosu, Japan

[2] Shinshu Univ, Nagano, Japan

来源：

FORMALIZED MATHEMATICS | 2008年 / 16卷 / 04期

关键词：

D O I：

10.2478/v10037-008-0039-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we formalized the notion of the integral of a complex-valued function considered as a sum of its real and imaginary parts. Then we defined the measurability and integrability in this context, and proved the linearity and several other basic properties of complex-valued measurable functions. The set of properties showed in this paper is based on [15], where the case of real-valued measurable functions is considered.

引用

页码：319 / 324

页数：6

共 50 条

[1] Integral of Real-Valued Measurable Function
Shidama, Yasunari
Endou, Noboru
FORMALIZED MATHEMATICS, 2006, 14 (04): : 143 - 152
[2] Uniqueness of feedforward complex-valued neural network with a given complex-valued function
Nitta, T
KNOWLEDGE-BASED INTELLIGENT INFORMATION ENGINEERING SYSTEMS & ALLIED TECHNOLOGIES, PTS 1 AND 2, 2001, 69 : 550 - 554
[3] SINGULAR INTEGRAL EQUATIONS WITH COMPLEX-VALUED KERNELS
TRJITZINSKY, WJ
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1947, 53 (01) : 58 - 58
[4] FCCNs: Fully Complex-valued Convolutional Networks using Complex-valued Color Model and Loss Function
Yadav, Saurabh
Jerripothula, Koteswar Rao
2023 IEEE/CVF INTERNATIONAL CONFERENCE ON COMPUTER VISION (ICCV 2023), 2023, : 10655 - 10664
[5] Complex-valued Function Approximation using a Fully Complex-valued RBF (FC-RBF) Learning Algorithm
Savitha, R.
Suresh, S.
Sundararajan, N.
IJCNN: 2009 INTERNATIONAL JOINT CONFERENCE ON NEURAL NETWORKS, VOLS 1- 6, 2009, : 320 - +
[6] Estimates for Fourier integral operators with complex-valued phase functions
Ruzhanskii, MV
RUSSIAN MATHEMATICAL SURVEYS, 2001, 56 (01) : 174 - 175
[7] Prediction of Complex-Valued Signals by Using Complex-Valued LMK Algorithm
Menguc, Engin Cemal
Acir, Nurettin
2017 25TH SIGNAL PROCESSING AND COMMUNICATIONS APPLICATIONS CONFERENCE (SIU), 2017,
[8] Is a Complex-Valued Stepsize Advantageous in Complex-Valued Gradient Learning Algorithms?
Zhang, Huisheng
Mandic, Danilo P.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 2016, 27 (12) : 2730 - 2735
[9] Nonlinear adaptive prediction of complex-valued signals by complex-valued PRNN
Goh, SL
Mandic, DP
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2005, 53 (05) : 1827 - 1836
[10] Complex-Valued Neural Network and Complex-Valued Backpropagation Learning Algorithm
Nitta, Tohru
ADVANCES IN IMAGING AND ELECTRON PHYSICS, VOL 152, 2008, 152 : 153 - 220

← 1 2 3 4 5 →