Related papers: Wavelet-Packet Content for Positive Operators
This paper investigates an iterative rank-one decomposition scheme for positive operators on a Hilbert space based on a residual-weighted congruence update. At each step the operator is compressed along a chosen unit vector while remaining…
We study the evolution of a positive operator under weighted residual maps determined by a finite family of orthogonal projections. Iterating these maps along the rooted tree of multi-indices produces a "weighted residual energy tree",…
In this article we study different aspects of Hermitian operators applying the concept of positive decompositions. On the one hand, we characterize the positivity of an Hermitian operator by means of a norm condition where the factors of…
We consider a class of infinite weighted metric trees obtained as perturbations of self-similar regular trees. Possible definitions of the boundary traces of functions in the Sobolev space on such a structure are discussed by using…
In this paper we study positive fixed points of Hammerstein integral operators with degenerate kernel in the cone of C[0, 1]. Problem on a number of positive fixed points of the Hammerstein integral operator leads to the study positive…
We study bounded weighted shifts on directed trees. We show that the set of multiplication operators associated with an injective weighted shift on a rooted directed tree coincides with the WOT/SOT closure of the set of polynomials of the…
This paper develops a nonlinear operator dynamic that progressively removes the influence of a prescribed feature subspace while retaining maximal structure elsewhere. The induced sequence of positive operators is monotone, admits an exact…
We study iterated weighted residual (WR) splittings generated by a positive operator $R_{0}\in B\left(H\right)_{+}$ and a finite family of contractions $C_{1},\dots,C_{m}$ in $B\left(H\right)$. The associated residual update $R\mapsto…
We propose an adaptive refinement algorithm to solve total variation regularized measure optimization problems. The method iteratively constructs dyadic partitions of the unit cube based on i) the resolution of discretized dual problems and…
Dual-tree wavelet decompositions have recently gained much popularity, mainly due to their ability to provide an accurate directional analysis of images combined with a reduced redundancy. When the decomposition of a random process is…
This paper studies the construction of a refinement kernel for a given operator-valued reproducing kernel such that the vector-valued reproducing kernel Hilbert space of the refinement kernel contains that of the given one as a subspace.…
The detail structure of the wave function is analyzed at various refinement levels using the methods of wavelet analysis. The eigenvalue problem of a model system is solved in granular Hilbert spaces, and the trajectory of the eigenstates…
This paper is devoted to an approximation problem for operators in Hilbert space, that appears when one tries to study geometrically the cascade algorithm in wavelet theory. Let $ H $ be a Hilbert space, and let $ \pi $ be a representation…
We develop a statistically robust framework for reconstructing metal--semiconductor contact regions using topological gradients. The inverse problem is formulated as the identification of an unknown contact region from boundary measurements…
In this paper we study an emerging class of neural networks based on the morphological operators of dilation and erosion. We explore these networks mathematically from a tropical geometry perspective as well as mathematical morphology. Our…
Decision trees with binary splits are popularly constructed using Classification and Regression Trees (CART) methodology. For binary classification and regression models, this approach recursively divides the data into two near-homogenous…
Using a prime element of a local field K of positive characteristic p, the concepts of multiresolution analysis (MRA) and wavelet can be generalized to such a field. We prove a version of the splitting lemma for this setup and using this…
Fine-tuning adapts pretrained networks to new objectives. Whether the resulting depth profile of representational change reflects an intrinsic property of the model or the magnitude of gradient flow has not been tested directly. We measure…
We study how iterated and composed completely positive maps act on operator-valued kernels. Each kernel is realized inside a single Hilbert space where composition corresponds to applying bounded creation operators to feature vectors. This…
It is shown that a positive (bounded linear) operator on a Hilbert space with trivial kernel is unitarily equivalent to a Hankel operator that satisfies double positivity condition if and only if it is non-invertible and has simple spectrum…