code: def shift_operator(
      x: FourierSeries, *, dx=[0], params=None
  ) -> FourierSeries:
      r"""Shifts the field by `dx` using the shift theorem in Fourier space.
  
      Args:
        x: The field to shift
        dx: The shift to apply
  
      Returns:
        A new field corresponding to the shifted input field.
      """
      if x.is_real:
          ffts = [jnp.fft.rfft, jnp.fft.irfft]
      else:
          ffts = [jnp.fft.fft, jnp.fft.ifft]
      k_vec = params["k_vec"]
  
      # Adding staggering
      if len(dx) == 1 and len(x.domain.N) != 1:
          dx = dx * len(x.domain.N)
  
      k_vec = [jnp.exp(1j * k * delta) for k, delta in zip(k_vec, dx)]
  
      new_params = jnp.zeros_like(x.params)
  
      def single_grad(axis, u):
          u = jnp.moveaxis(u, axis, -1)
          Fx = ffts[0](u, axis=-1)
          iku = Fx * k_vec[axis]
          du = ffts[1](iku, axis=-1, n=u.shape[-1])
          return jnp.moveaxis(du, -1, axis)
  
      for ax in range(x.domain.ndim):
          new_params = new_params.at[..., ax].set(
              single_grad(ax, x.params[..., ax])
          )
  
      return FourierSeries(new_params, x.domain), params
  
imports: from typing import List
  import numpy
  from jax import numpy
  from jaxdf.conv import reflection_conv
  from jaxdf.core import operator
  from jaxdf.discretization import Continuous, FiniteDifferences, FourierSeries, OnGrid
  from jaxdf.operators.differential import get_fd_coefficients
label_desc: Use image node_id 13 for calling a global function with example usage: shift_operator(x) and returns: FourierSeries,  params, jnp