Tootfinder

On the discrete Hilbert-type operators
Jianjun Jin
https://arxiv.org/abs/2505.22972 https://arxiv.org/pdf/2505.22972

On the discrete Hilbert-type operators
Recently, Bansah and Sehba studied in [3] the boundedness of a family of Hilbert-type integral operators, in which they characterized the $L^{p}-L^{q}$ boundedness of the operators for $1\leq p\leq q\leq \infty$. In this paper, we deal with the corresponding discrete Hilbert-type operators acting on the weighted sequence spaces. We establish some sufficient and necessary conditions for the $l^{p}-l^{q}$ boundedness of the operators for $1\leq p\leq q\leq \infty$. We find out that the conditions…

Discrete and Continuous Muttalib--Borodin process: Large deviations and Riemann--Hilbert analysis
Jonathan Husson, Guido Mazzuca, Alessandra Occelli
https://arxiv.org/abs/2505.23164

Discrete and Continuous Muttalib--Borodin process: Large deviations and Riemann--Hilbert analysis
In this paper, we study the asymptotic behaviour of plane partitions distributed according to a weighted $q^{Volume}$ Muttalib--Borodin ensemble. Specifically, we establish a Large Deviation principle for the discrete Muttalib--Borodin process, characterising the rate function. Furthermore, through Riemann--Hilbert analysis, we give an explicit expression for the asymptotic shape of the partition.

This https://arxiv.org/abs/2401.06584 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Dagger categories and the complex numbers: Axioms for the category of finite-dimensional Hilbert spaces and linear contractions
We unravel a deep connection between limits of real numbers and limits in category theory. Using a new variant of the classical characterisation of the real numbers, we characterise the category of finite-dimensional Hilbert spaces and linear contractions in terms of simple category-theoretic structures and properties that do not refer to norms, continuity, or real numbers. This builds on Heunen, Kornell, and Van der Schaaf's easier characterisation of the category of all Hilbert spaces and lin…

EILMELDUNG
Brückenbauexperte fordert keine Denkverbote beim Neubau der #Carolabrücke!
htt…

This https://arxiv.org/abs/2410.20448 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

New results related to cutters and to an extrapolated block-iterative method for finding a common fixed point of a collection of them
Given a Hilbert space and a finite family of operators defined on the space, the common fixed point problem (CFPP) is to find a point in the intersection of the fixed point sets of these operators. Instances of the problem have numerous applications in science and engineering. We consider an extrapolated block-iterative method with dynamic weights for solving the CFPP assuming the operators belong to a wide class of operators called cutters. Global convergence is proved in two different scenari…

This https://arxiv.org/abs/2410.03614 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Proudfoot-Speyer degenerations of scattering equations
We study scattering equations of hyperplane arrangements from the perspective of combinatorial commutative algebra and numerical algebraic geometry. We formulate the problem as linear equations on a reciprocal linear space and develop a degeneration-based homotopy algorithm for solving them. We investigate the Hilbert regularity of the corresponding homogeneous ideal and apply our methods to CHY scattering equations.

On General Principal Symmetric Ideals
Noah Walker
https://arxiv.org/abs/2505.21802 https://arxiv.org/pdf/2505.21802

On General Principal Symmetric Ideals
In a recent paper by Harada, Seceleanu, and Şega, the Hilbert function, betti table, and graded minimal free resolution of a general principal symmetric ideal are determined when the number of variables in the polynomial ring is sufficiently large. In this paper, we strengthen that result by giving a effective bound on the number of variables needed for their conclusion to hold. The bound is related to a well-known integer sequence involving partition numbers (OEIS A000070). Along the way, we …

1-D Schr\"odinger operator on a star graph with nondefinite weight function
Edison Leguizam\'on, Carsten Trunk, Mitsuru Wilson, Monika Winklmeier
https://arxiv.org/abs/2505.22901

1-D Schrödinger operator on a star graph with nondefinite weight function
On a star graph $G$ with $n = n_+ + n_-$ edges of unit length, we study the operator $-\frac{\mathrm{d}^2}{\mathrm{d} x^2}$ on $n_+$ and $\frac{\mathrm{d}^2}{\mathrm{d} x^2}$ on $n_-$ edges equipped with Dirichlet boundary conditions at the outer vertices and a Kirchhoff condition at the central vertex. We study the spectral properties of the corresponding indefinite Kirchhoff Laplacian on $G$ and we show that it is similar to a selfadjoint operator in the Hilbert space $L^2(G)$ and that its ei…

This https://arxiv.org/abs/2410.20448 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

New results related to cutters and to an extrapolated block-iterative method for finding a common fixed point of a collection of them
Given a Hilbert space and a finite family of operators defined on the space, the common fixed point problem (CFPP) is to find a point in the intersection of the fixed point sets of these operators. Instances of the problem have numerous applications in science and engineering. We consider an extrapolated block-iterative method with dynamic weights for solving the CFPP assuming the operators belong to a wide class of operators called cutters. Global convergence is proved in two different scenari…

Group Convolutional Neural Network Ground State of the Quantum Dimer Model
Ojasvi Sharma, Sandipan Manna, Prashant Shekhar Rao, G J Sreejith
https://arxiv.org/abs/2505.23728

Group Convolutional Neural Network Ground State of the Quantum Dimer Model
We estimate the ground state of the square lattice Quantum Dimer Model in a $\rm{p4m}$-symmetric Group Convolutional Neural Network (GCNN) representation and show that results in agreement with exact diagonalization (ED) and quantum Monte Carlo (QMC) can be obtained with a $\mathcal{L}=2$ layer network. In systems of linear size $L=8$ with Hilbert space dimension $3.1\times 10^8$, GCNN shows fidelity as high as $0.99999$ with ED. For $12\leq L\leq 32$, we find excellent agreement with QMC estim…

A warm welcome to all our guests for the
#RTG2491 Spring School on Decoupling and More
The registration is open in the #Hilbert room (entrance area).
#SpringSchool …

Factorization of positive definite kernels. Correspondences: $C^{*}$-algebraic and operator valued context vs scalar valued kernels
Palle E. T. Jorgensen, James Tian
https://arxiv.org/abs/2505.21037

Factorization of positive definite kernels. Correspondences: $C^{*}$-algebraic and operator valued context vs scalar valued kernels
We introduce and study a class $\mathcal{M}$ of generalized positive definite kernels of the form $K\colon X\times X\to L(\mathfrak{A},L(H))$, where $\mathfrak{A}$ is a unital $C^{*}$-algebra and $H$ a Hilbert space. These kernels encode operator-valued correlations governed by the algebraic structure of $\mathfrak{A}$, and generalize classical scalar-valued positive definite kernels, completely positive (CP) maps, and states on $C^{*}$-algebras. Our approach is based on a scalar-valued kernel …

Sampling Finite Unit Norm Tight Frames Using Symplectic Geometry
Mason Faldet, Clayton Shonkwiler
https://arxiv.org/abs/2505.22847 https://

Sampling Finite Unit Norm Tight Frames Using Symplectic Geometry
Unit-norm tight frames in finite-dimensional Hilbert spaces (FUNTFs) are fundamental in signal processing, offering optimal robustness to noise and measurement loss. In this paper we introduce the Eigenlift algorithm for sampling random FUNTFs. Our approach exploits the symplectic geometry of the FUNTF space, which we characterize as a symplectic reduction of frame space by a symmetry group. We then define a Hamiltonian torus action on this reduced space whose momentum map induces a fiber bundl…

On General Principal Symmetric Ideals
Noah Walker
https://arxiv.org/abs/2505.21802 https://arxiv.org/pdf/2505.21802

On General Principal Symmetric Ideals
In a recent paper by Harada, Seceleanu, and Şega, the Hilbert function, betti table, and graded minimal free resolution of a general principal symmetric ideal are determined when the number of variables in the polynomial ring is sufficiently large. In this paper, we strengthen that result by giving a effective bound on the number of variables needed for their conclusion to hold. The bound is related to a well-known integer sequence involving partition numbers (OEIS A000070). Along the way, we …

Für alle die in #Göttingen gerade noch Ideen für die Abendgestaltung suchen: Die Nacht der Bibliotheken ist noch in vollen Gange.
Man trifft sogar Überraschungsgäste wie den guten David #Hilbert im Heynesaal der historischen @…

This https://arxiv.org/abs/2503.24170 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Localization of operator-valued frames
We introduce a localization concept for operator-valued frames, where the quality of localization is measured by the associated operator-valued Gram matrix belonging to some suitable Banach algebra. We prove that intrinsic localization of an operator-valued frame is preserved by its canonical dual. Moreover, we show that the series associated to the perfect reconstruction of an operator-valued frame converges not only in the underlying Hilbert space, but also in a whole class of associated (qua…

Wir freuen uns sehr über die Ehrung von Göttingen als 77te "#EPS historic site" und insbesondere auch die reichlichen Erwähnungen von Mathematikern, wie #Hilbert, #Klein,

This https://arxiv.org/abs/2505.10246 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSC_…

An Algorithm for the Leading Monomials of a Minimal Groebner Basis of Generic Sequences
We present an efficient algorithm for computing the leading monomials of a minimal Groebner basis of a generic sequence of homogeneous polynomials. Our approach bypasses costly polynomial reductions by exploiting structural properties conjectured to hold for generic sequences-specifically, that their leading monomial ideals are weakly reverse lexicographic and that their Hilbert series follow a known closed-form expression. The algorithm incrementally constructs the set of leading monomials deg…