# Questions tagged [schwartz-distributions]

A distribution is a continuous linear functional on the space $\mathcal{C}^{\infty}_c$ of smooth (indefinitely differentiable) functions with compact support. Though they appeared in formal computations in the physics and engineering literature in the late $19^{th}$ century, their formal setting was brought up by the work of S. Sobolev and L. Schwartz in the middle of the $20^{th}$ century.

**2**

**1**answer

### Prove that a given distribution is tempered

**2**

**0**answers

### Does this formula correspond to a series representation of the Dirac delta function $\delta(x)$?

**3**

**1**answer

### Distribution boundary value of analytic function and wave front sets

**3**

**0**answers

### Functional derivative as a Tensor of Dirac deltas

**4**

**2**answers

### Function of moderate growth: history, motivation, and uses

**6**

**1**answer

### $GL_1(\mathcal{E}'(\mathbb{R}))$ open in $\mathcal{E}'(\mathbb{R})$?

**1**

**1**answer

### Pointwise functional derivative as partial derivative

**2**

**3**answers

### Integral representation of tempered distributions

**2**

**2**answers

### Representation of a Schwartz map in terms of a kernel

**0**

**2**answers

### A question about homogeneous distribution

**3**

**2**answers

### distributional divergence of the gravitational / Coulomb force close to the boundary

**6**

**1**answer

### Smoothness of family of distributions

**2**

**0**answers

### Less regular version of the Gaussian free field

**3**

**1**answer

### Mathematical meaning for the (continuous) Sine-Gordon transformation

**1**

**1**answer

### Did anyone ever introduce an “oscillating unity”?

**-1**

**3**answers

### on compact support distributions [closed]

**2**

**0**answers

### Structure theorem for distributions with support in a variety

**3**

**1**answer

### Division theorem for vector-valued distributions

**4**

**1**answer

### Convergence in $\sigma(\mathcal{E}',\mathcal{E})$ versus $\beta(\mathcal{E}',\mathcal{E})$

**0**

**2**answers

### Derivatives of delta function as a basis for distributions [closed]

**1**

**1**answer

### Kernel of the composition of operators

**0**

**0**answers

### S-familiy induced by an operator induces a Schwartz function

**2**

**1**answer

### Continuity of convolution on $\mathcal{D}'_+$

**2**

**0**answers

### Time derivative in parabolic Hölder spaces

**6**

**2**answers

### For which tempered distributions is the fractional derivative well-defined?

**6**

**2**answers

### Fourier coefficients of a periodic distribution?

**6**

**1**answer

### Research topics in Microlocal Analysis

**5**

**0**answers

### Is polar decomposition of a smooth map Sobolev?

**2**

**0**answers

### Is the Fourier transform of a measurable function as a tempered distribution necessarily a complex Borel measure?

**1**

**0**answers

### Characterizing geometrically Schwartz Kernels of pseudodifferential operators on a compact manifold

**8**

**4**answers

### Defining the value of a distribution at a point

**1**

**1**answer

### Interchanging Integration Order involving Fourier Transform

**1**

**0**answers

### Fourier inversion formula for compactly supported distributions

**4**

**2**answers

### Fourier transform of a Lorentz invariant generalized function

**5**

**0**answers

### Extension of Valdivia-Vogt isomorphism from $\mathscr{D}(K)$ to $\mathscr{E}'(K)$

**3**

**0**answers

### Entire analytic functions with entire analytic Fourier transform, and corresponding distributions

**1**

**2**answers

### Delta-distribution composed with a function from the Fourier representation

**1**

**1**answer

### Convolution with Schwartz class function

**0**

**0**answers

### is this explicit linear operator hypo-elliptic

**4**

**1**answer

### Is convolution jointly continuous on $\mathcal{E}'$?

**10**

**2**answers

### Trace on $\mathcal{S}(\mathbb{R}^k) \mathbin{\hat{\otimes}_\pi} \mathcal{S}'(\mathbb{R}^k)$

**0**

**1**answer

### Covergent net in $\mathcal{E}'(\mathbb{R})$ implies bounded?

**1**

**0**answers

### Dense versus sequentially dense in $\mathcal{E}’$

**7**

**2**answers

### On the Fourier-Laplace transform of compactly supported distributions

**1**

**2**answers

### A question arising in the distribution theory of L. Schwartz

**2**

**0**answers

### Theory of distributions on various domains

**1**

**1**answer

### Schwartz distributions, Colombeau algebra and applications

**3**

**1**answer

### About the Fourier transform of the logarithm function

**5**

**1**answer

### The division problem for tempered functions

**-1**

**2**answers