Controlled generalized fusion frame in the tensor product of Hilbert spaces

Ghosh, Prasenjit; Samanta, T. K.

doi:10.52737/18291163-2021.13.13-1-18

Cited by 7 publications

(6 citation statements)

References 21 publications

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“…P. Casazza and Chirstensen [10] have been generalized the Paley-Wiener perturbation theorem to perturbation of frame in Hilbert space. P. Ghosh and T. K. Samanta have studied perturbation of dual g-fusion frame and continuous controlled g-fusion frame in [18,21]. In this section, we will see that under some small perturbations, continuous controlled K-g-fusion frames constitute woven continuous controlled K-g-fusion frame.…”

Section: Perturbation Of Woven Continuous Controlled G-fusion Framementioning

confidence: 89%

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Weaving Continuous Controlled K-g-Gusion Frames in Hilbert Spaces

GHOSH,

SAMANTA

2024

KgJMat

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We introduce the notion of weaving continuous controlled K-g-fusion frame in Hilbert space. Some characterizations of weaving continuous controlled K-g-fusion frame have been presented. We extend some of the recent results of woven K-g-fusion frame and controlled K-g-fusion frame to woven continuous controlled K-g-fusion frame. Finally, a perturbation result of woven continuous controlled K-g-fusion frame has been studied.

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Section: Perturbation Of Woven Continuous Controlled G-fusion Framementioning

confidence: 89%

“…In recent times, controlled frames and their generalizations are also studied in continuous case by many researchers. P. Ghosh and T. K. Samanta studied continuous version of controlled g-fusion frame in [21].…”

Section: Definition 12 ([28]mentioning

confidence: 99%

Weaving Continuous Controlled K-g-Gusion Frames in Hilbert Spaces

GHOSH,

SAMANTA

2024

KgJMat

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“…It is noteworthy that the filters will execute operations in the complex number domain, whereby we have selected the Hilbert space as the space where the necessary complex operations will be performed [ 28 ]. It must also be considered that the dot product is the basis of forward propagation operations in deep learning.…”

Section: Methodsmentioning

confidence: 99%

A Fair Performance Comparison between Complex-Valued and Real-Valued Neural Networks for Disease Detection

2022

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Our aim is to contribute to the classification of anomalous patterns in biosignals using this novel approach. We specifically focus on melanoma and heart murmurs. We use a comparative study of two convolution networks in the Complex and Real numerical domains. The idea is to obtain a powerful approach for building portable systems for early disease detection. Two similar algorithmic structures were chosen so that there is no bias determined by the number of parameters to train. Three clinical data sets, ISIC2017, PH2, and Pascal, were used to carry out the experiments. Mean comparison hypothesis tests were performed to ensure statistical objectivity in the conclusions. In all cases, complex-valued networks presented a superior performance for the Precision, Recall, F1 Score, Accuracy, and Specificity metrics in the detection of associated anomalies. The best complex number-based classifier obtained in the Receiving Operating Characteristic (ROC) space presents a Euclidean distance of 0.26127 with respect to the ideal classifier, as opposed to the best real number-based classifier, whose Euclidean distance to the ideal is 0.36022 for the same task of melanoma detection. The 27.46% superiority in this metric, as in the others reported in this work, suggests that complex-valued networks have a greater ability to extract features for more efficient discrimination in the dataset.

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“…By identifying H / L F with M F in an obvious way, we obtain an inner product on M F . Then M F is a normed space with respect to the norm • F defined by For more details on frames in n-Hilbert spaces and their tensor products one can go through the papers [9,10,11].…”

Section: It Can Be Easily Verified Thatmentioning

confidence: 99%

Continuous frames in n-Hilbert spaces and their tensor products

Ghosh¹,

Samanta²

2022

Preprint

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We introduce the notion of continuous frame in n-Hilbert space which is a generalization of discrete frame in n-Hilbert space. The tensor product of Hilbert spaces is a very important topic in mathematics. Here we also introduce the concept of continuous frame for the tensor products of n-Hilbert spaces. Further, we study dual continuous frame and continuous Bessel multiplier in n-Hilbert spaces and their tensor products.

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Controlled generalized fusion frame in the tensor product of Hilbert spaces

Abstract: We present controlled by operators generalized fusion frame in the tensor product of Hilbert spaces and discuss some of its properties. We also describe the frame operator for a pair of controlled $g$-fusion Bessel sequences in the tensor product of Hilbert spaces.

Cited by 7 publications

References 21 publications

Weaving Continuous Controlled K-g-Gusion Frames in Hilbert Spaces

Weaving Continuous Controlled K-g-Gusion Frames in Hilbert Spaces

A Fair Performance Comparison between Complex-Valued and Real-Valued Neural Networks for Disease Detection

Continuous frames in n-Hilbert spaces and their tensor products

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