Related papers: The Schwartz functions and the derivation
As the title suggests, we give a formula for the $n^{th}$ derivative of a quotient of two functions, analogous to Leibniz's formula for the product. This particular note has remained unpublished since 2007 (available only my website),…
This paper has been withdrawn by the author.
The present article is devoted to the generalized Salem functions, the generailed shift operator, and certain related problems. A description of further investigations of the author of this article is given.These investigations (in terms of…
The paper has been withdrawn.
This paper has been withdrawn by the authors until some changes are made.
The explicit evaluation of the partition function in the Schwarzian theory is presented.
This paper has been withdrawn by the author, since some results of the paper have been already obtained in [J.~Lewandowski, Class. Quantum Grav. 9 (1992), no. 10, L147--L151.]
An explicit form of the functional measure on the factor space $Diff^{1}_{+}(S^{1})/SL(2,\textbf{R})$ is obtained that makes Schwarzian functional integrals calculus simpler and more transparent.
A space of entire functions of several complex variables rapidly decreasing on ${\mathbb R}^n$ and such that their growth along $i{\mathbb R}^n$ is majorized with the help of a family of weight functions is considered in this paper. For…
This paper has been withdrawn by the author due to inconsistency of the considered working hypothesis. The consistent treatment is presented in the last publications of the author.
Several relations are obtained among the Riemann zeta and Hurwitz zeta functions, as well as their products. A particular case of these relations give rise to a simple re-derivation if the important results of [11]. Also, a relation derived…
The paper has been withdrawn by the author.
This paper has been withdrawn by the authors because the paper is largely revised and improved, and to appear in Mechanics Research Communications.
This paper has been withdrawn. A significantly revised version will be posted in the near future.
This paper has been withdrawn by the author.
The paper has been withdrawn because the result of math.QA/0002057 "Deformation quantization with traces" holds only for a constant volume form.
The Schr\"odinger equation is universally accepted due to its excellent predictions aligning with observed results within its defined conditions. Nevertheless, it does not seem to possess the simplicity of fundamental laws, such as Newton's…
This paper has been withdrawn, not because of any errors (that we know of), but because rather than presenting our material as a series of 3 papers, as we originally intended, we have now combined them into one long paper, which is "A…
The paper considers (a) Representations of measure preserving transformations (``rotations'') on Wiener space, and (b) The stochastic calculus of variations induced by parameterized rotations $\{T_\theta w, 0 \le \theta \le \eps\}$:…
We study a cut-off function lemma in projective spaces. We believe that this is well-known. We provide the details of the computation for later uses.