query: Show that $v$ is harmonic and rotation invariant iff $v(z)=A\log |z|+B$ for some constants $A$ and $B$
positive_passages.docid: 17700
positive_passages.text: Find all possible functions, $F(r)$, harmonic in $2$ and $3$ dimensions,
negative_passages.docid: 145462
negative_passages.text: On the canonical isomorphism between $V$ and $V^{**}$
negative_passages.docid: 101786
negative_passages.text: Proving the Lorentz invariance of the Lorentz invariant phase space element
negative_passages.docid: 112329
negative_passages.text: Show that $d(z,a)=|\frac{z-a}{1-\overline{a}z}|$ is a metric on the unit disk
negative_passages.docid: 141794
negative_passages.text: Invariant subspaces of specific dimension
negative_passages.docid: 158852
negative_passages.text: If $\{v_1, v_2, v_3\}$ is an orthonormal basis of $\mathbb{R}^3$ and $v = a_1v_1 + a_2v_2 + a_3v_3$, can we have $|a_1| > 3$?
negative_passages.docid: 84999
negative_passages.text: $\exp(A)$ is orthogonal iff $A$ is skew symmetric
negative_passages.docid: 125680
negative_passages.text: Show that $(1+u) \log (1+u) - u \ge \frac{u^2}{2(1+u/3)} $
negative_passages.docid: 71442
negative_passages.text: How to prove $\det(I+uv^\intercal)=1+v^\intercal u$
negative_passages.docid: 88790
negative_passages.text: Positive harmonic function on $\mathbb{R}^n$ is a constant?
negative_passages.docid: 62640
negative_passages.text: Show a given analytic function is constant
negative_passages.docid: 75855
negative_passages.text: Show that $\det{(A + sxy^*)}$ is linear in $s$
negative_passages.docid: 7457
negative_passages.text: Prove that $J^+AJ$ has positive eigenvalues
negative_passages.docid: 108461
negative_passages.text: Sum of Harmonic Numbers
negative_passages.docid: 34702
negative_passages.text: Show $|A + uv^T| = (1 + v^T A^{-1} u) |A|$
negative_passages.docid: 94489
negative_passages.text: Mean value property implies harmonicity
negative_passages.docid: 128229
negative_passages.text: Proving that the transformation obtained from an adjoint pair is natural