اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe heat operator in infinite dimensions
201
0
0.0
(
0
)
تأليف
Brian C. Hall
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Let (H,B) be an abstract Wiener space and let mu_{s} be the Gaussian measure on B with variance s. Let Delta be the Laplacian (*not* the number operator), that is, a sum of squares of derivatives associated to an orthonormal basis of H. I will show that the heat operator exp(tDelta/2) is a contraction operator from L^2(B,mu_{s} to L^2(B,mu_{s-t}), for all t<s. More generally, the heat operator is a contraction from L^p(B,mu_{s}) to L^q(B,mu_{s-t}) for t<s, provided that p and q satisfy (p-1)/(q-1) leq s/(s-t). I give two proofs of this result, both very elementary.
قيم البحث
اقرأ أيضاً
We revisit the computation of the phase of the Dirac fermion scattering operator in external gauge fields. The computation is through a parallel transport along the path of time evolution operators. The novelty of the present paper compared with the
earlier geometric approach by Langmann and Mickelsson, [LM], is that we can avoid the somewhat arbitrary choice in the regularization of the time evolution for intermediate times using a natural choice of the connection form on the space of appropriate unitary operators.
We study the spectrum of the linear operator $L = - partial_{theta} - epsilon partial_{theta} (sin theta partial_{theta})$ subject to the periodic boundary conditions on $theta in [-pi,pi]$. We prove that the operator is closed in $L^2([-pi,pi])$ wit
h the domain in $H^1_{rm per}([-pi,pi])$ for $|epsilon| < 2$, its spectrum consists of an infinite sequence of isolated eigenvalues and the set of corresponding eigenfunctions is complete. By using numerical approximations of eigenvalues and eigenfunctions, we show that all eigenvalues are simple, located on the imaginary axis and the angle between two subsequent eigenfunctions tends to zero for larger eigenvalues. As a result, the complete set of linearly independent eigenfunctions does not form a basis in $H^1_{rm per}([-pi,pi])$.
In this work, the second-quantized version of the spatial-coordinate operator, known as the Newton-Wigner-Pryce operator, is explicitly given w.r.t. the massless scalar field. Moreover, transformations of the conformal group are calculated on eigenfu
nctions of this operator in order to investigate the covariance group w.r.t. probability amplitudes of localizing particles.
The main result of this paper is the extension of the Schur-Horn Theorem to infinite sequences: For two nonincreasing nonsummable sequences x and y that converge to 0, there exists a compact operator A with eigenvalue list y and diagonal sequence x i
f and only if y majorizes x (sum_{j=1}^n x_j le sum_{j=1}^n y_j for all n) if and only if x = Qy for some orthostochastic matrix Q. The similar result requiring equality of the infinite series in the case that the sequences x and y are summable is an extension of a recent theorem by Arveson and Kadison. Our proof depends on the construction and analysis of an infinite product of T-transform matrices. Further results on majorization for infinite sequences providing intermediate sequences generalize known results from the finite case. Majorization properties and invariance under various classes of stochastic matrices are then used to characterize arithmetic mean closed operator ideals.
We consider a system of anisotropic plates in the three-dimensional continuum, interacting via purely hard core interactions. We assume that the particles have a finite number of allowed orientations. In a suitable range of densities, we prove the ex
istence of a uni-axial nematic phase, characterized by long range orientational order (the minor axes are aligned parallel to each other, while the major axes are not) and no translational order. The proof is based on a coarse graining procedure, which allows us to map the plate model into a contour model, and in a rigorous control of the resulting contour theory, via Pirogov-Sinai methods.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
