Related papers: Partial trace of a full symmetrizer

In this paper, we consider the trace theorem for modulation spaces, alpha modulation spaces and Besov spaces. For the modulation space, we obtain the sharp results.

In this paper we discuss curvature tensors in the context of Absolute Parallelism geometry. Different curvature tensors are expressed in a compact form in terms of the torsion tensor of the canonical connection. Using the Bianchi identities…

A conducting two-dimensional periodic composite of two anisotropic phases with anisotropic, not necessarily symmetric, conductivity tensors is considered. By finding approximate representations for the relevant operators, an approximation…

We prove that the so-called first trace formula holds for all Schr\"odinger operators on the line with real-valued integrable potentials.

The trace test in numerical algebraic geometry verifies the completeness of a witness set of an irreducible variety in affine or projective space. We give a brief derivation of the trace test and then consider it for subvarieties of…

It is easily checkable if a given tensor is a B tensor, or a B$_0$ tensor or not. In this paper, we show that a symmetric B tensor can always be decomposed to the sum of a strictly diagonally dominated symmetric M tensor and several…

We derive an estimate of statistical error in calculating the trace of a large matrix by using random vector, and show that {\em random phase vector} gives the results with the smallest statistical error for a given basis set. This result…

We generalize the embedding formalism for conformal field theories to the case of general operators with mixed symmetry. The index-free notation encoding symmetric tensors as polynomials in an auxiliary polarization vector is extended to…

We prove perturbation results for traces on normed ideals in semifinite von Neumann algebra factors. This includes the case of Dixmier traces. In particular, we establish existence of spectral shift measures with initial operators being…

Differential geometries derived from tensor decompositions have been extensively studied and provided the foundations for a variety of efficient numerical methods. Despite the practical success of the tensor ring (TR) decomposition, its…

This paper studies symmetric tensor decompositions. For symmetric tensors, there exist linear relations of recursive patterns among their entries. Such a relation can be represented by a polynomial, which is called a generating polynomial.…

We first prove two new spectral properties for symmetric nonnegative tensors. We prove a maximum property for the largest H-eigenvalue of a symmetric nonnegative tensor, and establish some bounds for this eigenvalue via row sums of that…

Halved monotone triangles are a generalisation of vertically symmetric alternating sign matrices (VSASMs). We provide a weighted enumeration of halved monotone triangles with respect to a parameter which generalises the number of $-1$s in a…

The classification of all fourth-order anisotropic tensor classes for classical linear elasticity is well known. In this article, we review the related problem of explicitly computing the dimension and the expressions of the elements…

We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued decompositions of symmetric tensors, but here we focus on…

The length spectra of flat three-dimensional dielectric resonators of circular shape were determined from a microwave experiment. They were compared to a semiclassical trace formula obtained within a two-dimensional model based on the…

This paper discusses the problem of symmetric tensor decomposition on a given variety $X$: decomposing a symmetric tensor into the sum of tensor powers of vectors contained in $X$. In this paper, we first study geometric and algebraic…

We study the symmetric outer product decomposition which decomposes a fully (partially) symmetric tensor into a sum of rank-one fully (partially) symmetric tensors. We present iterative algorithms for the third-order partially symmetric…

We prove the murmuration phenomenon, which is a correlation between signs of functional equations and Fourier coefficients, in the case of modular forms in the weight aspect. We in particular improve the range of visibility of murmurations…

Changes of some unitarily invariant norms and anti-norms under the operation of partial trace are examined. The norms considered form a two-parametric family, including both the Ky Fan and Schatten norms as particular cases. The obtained…